Bridcutt, who made his name in the Championship during a four-year spell with Brighton, arrives on an emergency loan deal until the start of January.
The 26-year-old becomes the first player brought in by head coach Steve Evans and is keen to play regular football with the Whites after being frozen out at Sunderland where he has made 30 Premier League appearances.
He said: “This is a great opportunity for me to get some games.
“I’ve been speaking to the manager and he’s given me a great opportunity to come and play for a brilliant club.
“It’s been on and off for the last few weeks now. I’ve had a few other options, but from speaking to the manager he’s given me the confidence to come here and show what I can do.
“When the manager shows so much interest in you and puts so much faith in you, you always want to repay that with your performances. That is one of the main reasons why I have come here.”
Bridcutt will go straight into contention for United’s side at QPR on Saturday, but winger Buckley will not play as he returned to parent club Sunderland after being recalled from his emergency loan spell with United.
Buckley arrived at Elland Road at the start of October, but was limited to just four Championship appearances, three of which were as a substitute.