The 32-year-old saw his time with the Spanish giants cut short after tearing his anterior cruciate ligament early in March, with his contract expiring at the end of the last campaign.
Following the injury, an anticipated move to Monaco failed to materialise, while Valdes was also linked with United's Premier League rivals Liverpool.
He will now continue his recovery with United after being offered the chance by his former coach at Barca Louis van Gaal.
With Anders Lindegaard and Ben Amos currently providing David de Gea with competition for the number one spot, the arrangement will likely fuel rumours of a permanent move for Valdes.
The World Cup winner won a host of titles during his time at Camp Nou, with the player's agent suggesting previously his client would be "at a big team before Christmas".
While reports emerged recently that Valdes turned down the chance of a trial at Anfield, his representative Gines Carvajal stated such a proposal was never on the table.
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
