Horseman joined United in the summer as U21 assistant coach, but has already left to become player development coach with Arsenal.
Horseman will be in charge of Arsenal U19s for the UEFA Youth League and National Cup tournaments.
Gunners academy chief Per Mertesacker said: "We are really pleased to welcome David into our academy. He has a detailed knowledge of the game and will bring his wealth of footballing experience into the club to help progress both our staff and players alike.
“As a person, he will fit into our environment and culture perfectly, and will continue to help us drive our vision for the future. I look forward to seeing how he brings his skills to life on and off the pitch, and, in turn, help to challenge and care for our boys.”
David said: “I'm absolutely delighted to be joining the Arsenal academy. It's a fantastic opportunity, and I’m really looking forward to supporting the development of the players while also leading the UEFA Youth League and EFL Trophy teams.
“I can’t wait to get started and contribute to the exciting work already being done here at Arsenal.”