Buttner's move was announced via the Russian club on Monday, although no details of the deal were given.
However, a day after confirming the big-money signing of England full-back Luke Shaw, United have now also announced the transfer.
A statement on their official website read: "Everybody at Old Trafford would like to thank Alex for his service and wish him well for his new career in Russia."
Such sentiments are hardly a reciprocation of what Buttner himself said earlier in the week.
The 25-year-old appeared to take a thinly-veiled swipe at Louis van Gaal's men when claiming he was moving to "win trophies and play in the Champions League" - an apparent reference to the fact United will be absent from Europe's premier competition for the first time in 19 years next season.