City defender Karleigh joins on loan.
The Bristol City centre half has signed a loan deal to keep him in north Essex until the end of the season.
Boss Tony Humes has made no secret of the fact that he wanted defensive cover for the U's, following the departure of Kaspars Gorkss at the end of January.
Osborne has a wealth of experience at League One level, having started his career at Brentford, before moving to Millwall and subsequently Bristol City.
He is expected to go straight into the squad for the Doncaster game, with the U's keen to build on the victory over Osborne's parent club last weekend.