The Scotland international replaces former centre back Sol Bamba who left the club by mutual consent last week.
A delighted Bridcutt said: “It’s a real honour, the manager has shown great faith in me by giving me the captaincy.”
The former Sunderland and Brighton midfielder has made 29 appearances since initially moving to Elland Road on loan from Sunderland in November 2015.
He also went on to make his first appearance for Scotland for three years when he featured for Gordon Strachan’s side in their 1-0 home win against Denmark.
Bridcutt eventually moved to the Whites permanently last month, signing a two-year deal which will keep him at Leeds until the end of the 2017-18 season.
Despite the increased pressure put upon him by becoming captain, the new skipper believes that it will bring the best out of him
He said: “It puts a little bit more pressure on me but that’s something I like.
“I’ve always been a player that’s thrived under pressure and I think that’s the way to get the best out of me.”
Sol Bamba – No hard feelings: Pages 42-43