The Russians confirmed the Dutch full-back had joined the club on on Monday, but details of the transfer and the player's contract have yet to be revealed.
The 25-year-old has already joined up with his new team-mates and will be present at Dinamo's training camp in Austria.
United will not compete in European football next season after finishing a lowly seventh in the Premier League last season.
And Buttner, who made only 28 appearances at United after joining from Vitesse in 2012, believes he has a better chance of success in the Russian capital.
"I want to play in the Champions League and win trophies," Buttner told Dinamo's official website.
"Dinamo are building a very strong team and I am sure that we will be good enough to try and win the league title this season.
"This is my first time in Moscow and I will need time to adjust with my family. They flew out with me, so it would be easier to adapt.
"The training ground also has fantastic facilities. I am happy that I joined Dinamo."
