The 16-year-old will see his contract at FC Zurich expire at the end of the season, and he has chosen Old Trafford as his next destination.
The Swiss youth sensation can move for a small compensation fee, and United are set to offer him an attractive package to make the switch.
A number of other top European clubs were thought to be desperate to sign the talented teenager.
Manchester United are set for a busy summer in the transfer market, with David Moyes tasked with rebuilding the side after a season which has seen them struggle outside the top four.
Moyes is desperate to strengthen the United midfield, and while Mfomo is considered for the future, the Scot is hoping to sign Hoffenheim midfielder Roberto Firmino.
The Brazilian playmaker is reportedly considering a summer move, and may be available for around £12.5million.
Meanwhile, Robin van Persie may be allowed to leave the club in the summer, should United complete the signing of £58million rated forward Edinson Cavani.