Best way to convert callback-based async method to awaitable task

What would be the best way to convert/wrap a "classic" asynchronous method that uses a callback to something that returns a (awaitable) Task?

For example, given the following method:

public void GetStringFromUrl(string url, Action<string> onCompleted);

The only way I know of to wrap this into a method returning a task is:

public Task<string> GetStringFromUrl(string url)
{
     var t = new TaskCompletionSource<string>();

     GetStringFromUrl(url, s => t.TrySetResult(s));

     return t.Task;
}

Is this the only way to accomplish this?

And is there a way to wrap the call to GetStringFromUrl(url,callback) in the task itself (i.e. the call itself would run inside the task instead of synchronously)