Use the java.util.concurrent.TimeUnit class:

String.format("%d min, %d sec", 
    TimeUnit.MILLISECONDS.toMinutes(millis),
    TimeUnit.MILLISECONDS.toSeconds(millis) - 
    TimeUnit.MINUTES.toSeconds(TimeUnit.MILLISECONDS.toMinutes(millis))
);

Note: TimeUnit is part of the Java 1.5 specification, but toMinutes was added as of Java 1.6.

To add a leading zero for values 0-9, just do:

String.format("%02d min, %02d sec", 
    TimeUnit.MILLISECONDS.toMinutes(millis),
    TimeUnit.MILLISECONDS.toSeconds(millis) - 
    TimeUnit.MINUTES.toSeconds(TimeUnit.MILLISECONDS.toMinutes(millis))
);

If TimeUnit or toMinutes are unsupported (such as on Android before API version 9), use the following equations:

int seconds = (int) (milliseconds / 1000) % 60 ;
int minutes = (int) ((milliseconds / (1000*60)) % 60);
int hours   = (int) ((milliseconds / (1000*60*60)) % 24);
//etc...

Uhm... how many milliseconds are in a second? And in a minute? Division is not that hard.

int seconds = (int) ((milliseconds / 1000) % 60);
int minutes = (int) ((milliseconds / 1000) / 60);

Continue like that for hours, days, weeks, months, year, decades, whatever.

I would not pull in the extra dependency just for that (division is not that hard, after all), but if you are using Commons Lang anyway, there are the DurationFormatUtils.

Example Usage (adapted from here):

import org.apache.commons.lang3.time.DurationFormatUtils

public String getAge(long value) {
    long currentTime = System.currentTimeMillis();
    long age = currentTime - value;
    String ageString = DurationFormatUtils.formatDuration(age, "d") + "d";
    if ("0d".equals(ageString)) {
        ageString = DurationFormatUtils.formatDuration(age, "H") + "h";
        if ("0h".equals(ageString)) {
            ageString = DurationFormatUtils.formatDuration(age, "m") + "m";
            if ("0m".equals(ageString)) {
                ageString = DurationFormatUtils.formatDuration(age, "s") + "s";
                if ("0s".equals(ageString)) {
                    ageString = age + "ms";
                }
            }
        }
    }
    return ageString;
}   

Example:

long lastTime = System.currentTimeMillis() - 2000;
System.out.println("Elapsed time: " + getAge(lastTime)); 

//Output: 2s

Note: To get millis from two LocalDateTime objects you can use:

long age = ChronoUnit.MILLIS.between(initTime, LocalDateTime.now())

Either hand divisions, or use the SimpleDateFormat API.

long start = System.currentTimeMillis();
// do your work...
long elapsed = System.currentTimeMillis() - start;
DateFormat df = new SimpleDateFormat("HH 'hours', mm 'mins,' ss 'seconds'");
df.setTimeZone(TimeZone.getTimeZone("GMT+0"));
System.out.println(df.format(new Date(elapsed)));

Edit by Bombe: It has been shown in the comments that this approach only works for smaller durations (i.e. less than a day).

Joda-Time

Using Joda-Time:

DateTime startTime = new DateTime();

// do something

DateTime endTime = new DateTime();
Duration duration = new Duration(startTime, endTime);
Period period = duration.toPeriod().normalizedStandard(PeriodType.time());
System.out.println(PeriodFormat.getDefault().print(period));

For those who looking for Kotlin code:

fun converter(millis: Long): String =
        String.format(
            "%02d : %02d : %02d",
            TimeUnit.MILLISECONDS.toHours(millis),
            TimeUnit.MILLISECONDS.toMinutes(millis) - TimeUnit.HOURS.toMinutes(
                TimeUnit.MILLISECONDS.toHours(millis)
            ),
            TimeUnit.MILLISECONDS.toSeconds(millis) - TimeUnit.MINUTES.toSeconds(
                TimeUnit.MILLISECONDS.toMinutes(millis)
            )
        )

Sample output: 09 : 10 : 26

Firstly, System.currentTimeMillis() and Instant.now() are not ideal for timing. They both report the wall-clock time, which the computer doesn't know precisely, and which can move erratically, including going backwards if for example the NTP daemon corrects the system time. If your timing happens on a single machine then you should instead use System.nanoTime().

Secondly, from Java 8 onwards java.time.Duration is the best way to represent a duration:

long start = System.nanoTime();
// do things...
long end = System.nanoTime();
Duration duration = Duration.ofNanos(end - start);
System.out.println(duration); // Prints "PT18M19.511627776S"
System.out.printf("%d Hours %d Minutes %d Seconds%n",
        duration.toHours(), duration.toMinutes() % 60, duration.getSeconds() % 60);
// prints "0 Hours 18 Minutes 19 Seconds"

This is easier in Java 9:

    Duration elapsedTime = Duration.ofMillis(millisDiff );
    String humanReadableElapsedTime = String.format(
            "%d hours, %d mins, %d seconds",
            elapsedTime.toHours(),
            elapsedTime.toMinutesPart(),
            elapsedTime.toSecondsPart());

This produces a string like 0 hours, 39 mins, 9 seconds.

If you want to round to whole seconds before formatting:

    elapsedTime = elapsedTime.plusMillis(500).truncatedTo(ChronoUnit.SECONDS);

To leave out the hours if they are 0:

    long hours = elapsedTime.toHours();
    String humanReadableElapsedTime;
    if (hours == 0) {
        humanReadableElapsedTime = String.format(
                "%d mins, %d seconds",
                elapsedTime.toMinutesPart(),
                elapsedTime.toSecondsPart());

    } else {
        humanReadableElapsedTime = String.format(
                "%d hours, %d mins, %d seconds",
                hours,
                elapsedTime.toMinutesPart(),
                elapsedTime.toSecondsPart());
    }

Now we can have for example 39 mins, 9 seconds.

To print minutes and seconds with leading zero to make them always two digits, just insert 02 into the relevant format specifiers, thus:

    String humanReadableElapsedTime = String.format(
            "%d hours, %02d mins, %02d seconds",
            elapsedTime.toHours(),
            elapsedTime.toMinutesPart(),
            elapsedTime.toSecondsPart());

Now we can have for example 0 hours, 39 mins, 09 seconds.

There is a problem. When milliseconds is 59999, actually it is 1 minute but it will be computed as 59 seconds and 999 milliseconds is lost.

Here is a modified version based on previous answers, which can solve this loss:

public static String formatTime(long millis) {
    long seconds = Math.round((double) millis / 1000);
    long hours = TimeUnit.SECONDS.toHours(seconds);
    if (hours > 0)
        seconds -= TimeUnit.HOURS.toSeconds(hours);
    long minutes = seconds > 0 ? TimeUnit.SECONDS.toMinutes(seconds) : 0;
    if (minutes > 0)
        seconds -= TimeUnit.MINUTES.toSeconds(minutes);
    return hours > 0 ? String.format("%02d:%02d:%02d", hours, minutes, seconds) : String.format("%02d:%02d", minutes, seconds);
}

DurationFormatUtils.formatDurationHMS(long)

Use java.util.concurrent.TimeUnit, and use this simple method:

private static long timeDiff(Date date, Date date2, TimeUnit unit) {
    long milliDiff=date2.getTime()-date.getTime();
    long unitDiff = unit.convert(milliDiff, TimeUnit.MILLISECONDS);
    return unitDiff; 
}

For example:

SimpleDateFormat sdf = new SimpleDateFormat("yy/MM/dd HH:mm:ss");  
Date firstDate = sdf.parse("06/24/2017 04:30:00");
Date secondDate = sdf.parse("07/24/2017 05:00:15");
Date thirdDate = sdf.parse("06/24/2017 06:00:15");

System.out.println("days difference: "+timeDiff(firstDate,secondDate,TimeUnit.DAYS));
System.out.println("hours difference: "+timeDiff(firstDate,thirdDate,TimeUnit.HOURS));
System.out.println("minutes difference: "+timeDiff(firstDate,thirdDate,TimeUnit.MINUTES));
System.out.println("seconds difference: "+timeDiff(firstDate,thirdDate,TimeUnit.SECONDS));

This topic has been well covered, I just wanted to share my functions perhaps you can make use of these rather than importing an entire library.

    public long getSeconds(ms) {
        return (ms/1000%60);
    }
    public long getMinutes(ms) {
        return (ms/(1000*60)%60);
    }
    public long getHours(ms) {
        return ((ms/(1000*60*60))%24);
    }

I needed to convert the entire milliseconds to seconds in a project, in case you need this functionality here you go:

    public long convertToSeconds(long ms) {
        //                    hours                       minutes              seconds
        return ((((ms/(1000*60*60))%24)*60)*60) + ((ms/(1000*60) %60)*60) + (ms/1000%60);
    }