Merge Video from one MP4 with Audio from another MP4 - How?

Is there a way to merge (preferably with Handbrake) to merge the video from one MP4 file with the audio of another MP4 file? And set a track offset while doing it?

In VLC, you can:
1. Select Media menu
2. Select Open (advanced) menu item
3. Click Add and pick the video file you want to play
4. Tick the Show More Options tickbox
5. Tick the Play Another Media Synchonously (extra audio file, ...)
6. Click Browse button to pick the audio file you want to play


then


7. Select Tools menu
8. Select Preferences menu item
9. Tick the All choice in the Show Settings box
10. Scroll to Audio
11. Set Audio Desynchonization Compensation to your desired offset value.


Doing this will PLAY the video file and audio file that you want - but it's just a temporary solution.


I want to know how to reencode / merge the two files together permanently. How can you do that?