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.
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