The club will officially change its name "once the formalities regarding the share transfer have been completed and approved by the League."
Wimbledon moved to Milton Keynes in September 2003 but were relegated to Nationwide Division Two at the end of last season.
They currently play at the National Hockey Stadium, but hope to eventually move to a new 28,000-seater ground in Denbigh.
Wimbledon moved to Milton Keynes in 2001 and the FA took more than a year to approve the move. The decision was criticised by many supporters across the country as US-style "franchising", a common practice whereby top sports teams are regularly bought and sold and move from city to city.
In the summer of 2002, outraged Dons fans formed a breakaway non-League club, AFC Wimbledon, which joined the Combined Counties League.
Despite the independent commission's ruling that the formation of such a club "would not be in the wider interests of football", AFC Wimbledon have thrived, climbing to the Ryman First Division.
A statement from the consortium that now owns the franchised club said: "We feel the name 'Milton Keynes Dons FC' will represent the past, present and future and place the club at the heart of its new community. The FA Commission recommended that the club should always retain a link with its former identity."
They'll be calling it 'footy' next you watch.