The Slovakia international goalkeeper joined the Red Devils on a temporary basis in September and made two appearances under Erik ten Hag.
Dúbravka, who joined the Magpies from Czech side Sparta Prague, initially on loan, in January 2018 has made 130 competitive appearances during his time on Tyneside, recording 37 clean sheets in the English top-flight.
He won the club's 2019/20 Player of the Year award as well as the 2018 North East Football Writers' Association Player of the Year, and recorded eight shut-outs last term.
And he will now provide further competition for Nick Pope, who kept his ninth league clean sheet of the season - the most in the Premier League - in Saturday's 0-0 draw with Leeds.