The 26-year-old Liverpool-born right-back made 72 appearances for Derby County during a two-year spell at Pride Park, and completed a stint on loan at Sheffield United last term.
Connolly, who began his career at Plymouth Argyle, is thought to have moved to the West Yorkshire club on a free transfer, despite having a year to run on his Derby contract.
He told Leeds' official website: "I followed Leeds' fortunes last season and was obviously hoping the club would get to the Championship. There were others, but Leeds gave me a concrete offer. I spoke to the gaffer (Simon Grayson) while I was on holiday and we had a long chat.
"He didn't have to sell the club - you don't have to sell Leeds - he said he wanted me, and he seems like he will be a really good guy to work with. I know I'm competing with other players who have played right-back, and I'm looking forward to it.
"I can't wait to express myself. I'm not going to dribble past 11 players and chip it in the top corner, but I'll do my basics right, get in a tackle, push forward, and look to deliver good crosses."
Grayson added: "Paul brings plenty of experience and knowhow to the squad. He has made a lot of appearances at this level for both Plymouth and Derby. He has captained teams in the Championship and is a good addition to our squad."