The deal means the Premier League club now wholly own the station, which is available via subscription in the UK and in 57 countries worldwide.
United described the purchase as a "strategic acquisition" which will allow them complete control of content and distribution.
Commercial director Richard Arnold said: "The acquisition of Sky's stake is great news for all of our fans who watch us around the globe, MUTV, its staff and the club.
"We look forward to continuing to enhance our media proposition and distribution capabilities in the years to come, and delivering some of the best and most compelling content to our 659 million followers.
"Sky has been an active and highly-valued partner since the channel's inception and has helped to build the best and most-watched club football channel in the world.
"We will continue to have a close relationship with Sky in the future."
MUTV was set up in 1998 as a three-way venture between United and broadcasters Sky and ITV.
Having acquired considerable in-house expertise, United bought ITV's stake in 2007 and the latest move is considered natural progression.
The channel costs £6 per month to UK viewers via cable or satellite.
- Mergers, Acquisitions & Takeovers