Angha will move to Germany on a Bosman at the end of the season.
"He has shown his potential in London and will make the next steps in his development at FCN. We're delighted to have signed such an interesting, young player.
"We've had our eye on him for a long time, he matches our idea of a player who could flourish."
Angha added: "I had a great time in London and thank Arsenal for everything they've done. Now I'm looking forward to the challenge of playing for FCN."