Everton boss Moyes, who announced earlier he would be leaving the club after 11 years in charge, was the hot favourite to take over from his fellow Scot at United and has signed a six-year contract from July 1.
"When we discussed the candidates that we felt had the right attributes we unanimously agreed on David Moyes," Ferguson, who is staying at United as an ambassador and director, said in a statement.
"David is a man of great integrity with a strong work ethic. I've admired his work for a long time and approached him as far back as 1998 to discuss the position of assistant manager here.
"He was a young man then at the start of his career and has since gone on to do a magnificent job at Everton. There is no question he has all the qualities we expect of a manager at this Club."
Moyes is braced for the tough job of following Britain's most successful manager, who is retiring at the end of the season after winning two Champions Leagues, 13 league titles, five FA Cups in more than 26 years at United.
"It's a great honour to be asked to be the next manager of Manchester United. I am delighted that Sir Alex saw fit to recommend me for the job. I have great respect for everything he has done and for the Football Club," the 50-year-old said.
"I know how hard it will be to follow the best manager ever, but the opportunity to manage Manchester United isn't something that comes around very often and I'm really looking forward to taking up the post next season."
Moyes will remain in charge for Everton's final two Premier League games of the season against West Ham United and Chelsea.
"I have had a terrific job at Everton, with a tremendous chairman and board of directors and a great set of players," he added.
"Between now and the end of the season, I will do everything in my power to make sure we finish as high as possible in the table."
While Moyes shares the steely glare, work ethic and Scottish accent of Ferguson, he has none of the trophies.
The closest he came to silverware with Everton was the 2009 FA Cup, in which they lost 2-1 to Chelsea in the final having taken a first-minute lead.
He is also a Champions League novice, having only once guided Everton to a place in Europe's elite competition although they never reached the group stage, going out 4-2 on aggregate to Villarreal in the third qualifying round in 2005/06.
Despite the lack of cups and titles, Moyes is seen by his new club as having the right qualities for the top job.
"I have always said that we wanted the next manager to be a genuine Manchester United man. In David Moyes, we have someone who understands the things that make this such a special club," Bobby Charlton, former United player and current board member, said.
"We have secured a man who is committed to the long term and will build teams for the future as well as now. Stability breeds success.
"David has tremendous strength of character and recognises the importance of bringing young players through and developing them alongs
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.