The deal sees the former Newcastle United Goalie join up on an initial loan worth £2million.
There is a £6million obligatory buy clause inserted in deal if the veteran hits a number of appearances for United.
The deal brings an end to Man Utd’s search for a goalkeeper.
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The Manchester club had, earlier, set sights on Frankfurt’s Kevin Trapp.
The deal proved abortive, though, as Frankfurt never looked willing to entertain any negotiations for their shot-stopper.
Dúbravka will now vie for first team spots with fellow Keepers, David De Gea and Tom Heaton.