Dynamo's media office said a few technical details needed to be resolved before the contract could be finalised, without releasing any further information on the transfer.
Buttner has already joined up with his new team and will travel to their training camp in Austria.
"I want to play in the Champions League and win trophies," Buttner said on Dynamo's official website. "Dynamo 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 Dynamo."
Buttner's Champions League remark could be interpreted as a swipe at United, who failed to qualify for Europe last season under David Moyes.
Last week he expressed his dismay at new manager Louis van Gaal's apparent lack of faith him him.
He said: "Van Gaal never gave me the chance in the Dutch national team, despite being voted man of the match 14 times at Manchester United."
The Dutchman was unable to nail down a regular a first team spot, playing only 13 Premier League games during his stay at Manchester United and starting just 23 matches in all competitions.
Last season, the Red Devils suffered a dismal campaign finishing down in seventh place and for the first time in 25 years, missed out on European qualification.
After dismissing Moyes just 10 months into his first season in charge of the club, Dutch national coach Van Gaal was recruited as his replacement and will take over at the conclusion of the World Cup in Brazil.
Dynamo Moscow finished in fourth place last season and qualified for the Europa League.
- Sports & Recreation