Joel Glazer said: "I am very pleased David has agreed to lead Manchester United into the future.
"His hard working style and steely determination are characteristics we value at the Club. He has impressed as a coach for many years now and we strongly believe he will be able to take up from where Alex is leaving off by continuing this Club's tradition of flair football played by exciting, world class players."
And Avie Glazer added: "The search for a new manager has been very short. Alex was very clear with his recommendation and we are delighted that David has agreed to accept the job.
"He comes to us with excellent credentials and a strong track record. I know he is keen to get started and Ed will be sitting down with him as soon as the season is over to discuss plans for the summer and beyond."