How to perform a fade animation on Activity transition?

you can also add animation in your activity, in onCreate method like below becasue overridePendingTransition is not working with some mobile, or it depends on device settings...

View view = findViewById(android.R.id.content);
Animation mLoadAnimation = AnimationUtils.loadAnimation(getApplicationContext(), android.R.anim.fade_in);
mLoadAnimation.setDuration(2000);
view.startAnimation(mLoadAnimation);

You could create your own .xml animation files to fade in a new Activity and fade out the current Activity:

fade_in.xml

<?xml version="1.0" encoding="utf-8"?>
<alpha xmlns:android="http://schemas.android.com/apk/res/android"
           android:interpolator="@android:anim/accelerate_interpolator"
           android:fromAlpha="0.0" android:toAlpha="1.0"
           android:duration="500" />

fade_out.xml

<?xml version="1.0" encoding="utf-8"?>
<alpha xmlns:android="http://schemas.android.com/apk/res/android"
           android:interpolator="@android:anim/accelerate_interpolator"
           android:fromAlpha="1.0" android:toAlpha="0.0"
           android:fillAfter="true"
           android:duration="500" />

Use it in code like that: (Inside your Activity)

Intent i = new Intent(this, NewlyStartedActivity.class);
startActivity(i);
overridePendingTransition(R.anim.fade_in, R.anim.fade_out);

The above code will fade out the currently active Activity and fade in the newly started Activity resulting in a smooth transition.

UPDATE: @Dan J pointed out that using the built in Android animations improves performance, which I indeed found to be the case after doing some testing. If you prefer working with the built in animations, use:

overridePendingTransition(android.R.anim.fade_in, android.R.anim.fade_out);

Notice me referencing android.R instead of R to access the resource id.

UPDATE: It is now common practice to perform transitions using the Transition class introduced in API level 19.

Just re-posting answer by oleynikd because it's simple and neat

Bundle bundle = ActivityOptionsCompat.makeCustomAnimation(getContext(),
    android.R.anim.fade_in, android.R.anim.fade_out).toBundle(); 
startActivity(intent, bundle);

To animate while pressing back button,

override fun onNavigateUp(): Boolean {
    return super.onNavigateUp()
    overridePendingTransition(android.R.anim.fade_in, android.R.anim.fade_out)
}

override fun onBackPressed() {
    super.onBackPressed()
    overridePendingTransition(android.R.anim.fade_in, android.R.anim.fade_out)