The 25-year-old Dutchman was restricted to 15 appearances for United last season with compatriot Patrice Evra producing a string of impressive performances at left back.
With Buttner expressing his concern last month over his United future because of new manager Louis Van Gaal, along with the recent arrival of Luke Shaw, it was clear he was surplus to requirements at Old Trafford.
A statement on United's website read: "Manchester United has finalised the sale of Alex Buttner to Dynamo Moscow for an undisclosed fee.
"Everybody at Old Trafford would like to thank Alex for his service and wish him well for his new career in Russia."
Buttner becomes the third defender to leave United this summer after Rio Ferdinand and Nemanja Vidic.
It is understood the Russian club have paid £4.4million up front for the player, with the fee set to climb to £5.6million depending on appearances
United paid just under £4million for Buttner when they signed him from Vitesse Arnhem in August 2012. He scored on his debut against Wigan and also found the net in Sir Alex Ferguson's final game in charge, but he was never able to dislodge Evra as first-choice left-back.