Bruce had spent the past four years with Ipswich, but had a spell on loan at Leicester City in the second half of last season and has been allowed to move on by Roy Keane.
The Ipswich manager's Leeds counterpart Simon Grayson is delighted with the deal after making Bruce his seventh signing since clinching promotion from League One.
"Alex is going to be a good member of the squad. He can play at centre-back, right-back, and as a holding midfielder," Grayson told the club's official website.
"We felt we were short in those areas at this moment and we're delighted he's come.
"He's got a lot of experience, he's played in the Championship and the Premiership and he's what we want - a player who knows the division, is hungry and wants to be successful.
"We tried to sign him a year ago when we were in League One. Ipswich wouldn't let him go then we got a call a week ago to say he was available, and everything got agreed."