The Red Devils have paid £200,000 up front for the midfield man but further installments, depending upon his progress, could see the fee rise to as much as £1 million.
Chelsea and Arsenal were also believed to be hotly pursuing the 16-year-old, who has impressed for The Dons' Under-17 and Under-19 teams.
"We spoke to Stuart Murdoch and the management about Lee," administrator Nick Wood told skysports.com. "And we agreed to let him go.
"We would ideally have liked to keep him ourselves and brought him on, and possibly sold him on for a bigger fee than what we have received.
"But we needed the money and it is just too good to turn down."
Martin only signed an academy contract with Wimbledon in the summer but had already featured for the Milton Keynes-based club's reserves.
United agreed a fee with the First Division side to avoid heading for a tribunal.
Of course, Martin is the namesake of a famous name in United's history - the full back who was the surprise matchwinner in the 1990 FA Cup final replay against Crystal Palace.
