The 33-year-old centre-back has agreed a two-year deal after the Leith side agreed a nominal fee with Bradford.
Hibs are in desperate need of extra bodies ahead of their Scottish Premiership opening clash with Motherwell on Sunday following their 7-0 Europa League humiliation at the hands of Sweden's Malmo.
Fenlon said: "Michael is a quality defender, who knows the league well and we're really pleased to be able to add him to the squad.
"His experience will also help the younger players around him and Jimmy Nicholl, who worked with him at Kilmarnock, recommended him.
"We believe Michael will bring four qualities to the team - size, physicality, experience and leadership.
"Those attributes will add further strength to our squad for the start of the new season."
Nelson, who won the League Cup with Kilmarnock during his spell at Rugby Park, added: "I'm delighted to sign for Hibs; it's a great move for me and I can't wait to get started back playing in the Scottish Premiership.
"The move came around pretty quickly, but as soon as the initial contact was made, I was keen to the get the deal done.
"I had no hesitation about joining Hibs and I'm really excited about helping the team to succeed this season.
"Obviously I knew Jimmy Nicholl before from my time at Kilmarnock and enjoyed working with him.
"I was also impressed with what the manager, Pat Fenlon had to say about what he wants to achieve here at Hibs and I'm excited about being a part of it."
- Sports & Recreation
- Scottish Premiership
- Jimmy Nicholl