"Ask anyone who's been around him, Scott's passion and energy is contagious," Bulldogs coach Kirby Smart said in a statement. "Special Teams Coordinator is a great fit as he'll be working with all position groups. His knowledge and experience elevates our entire program, and we're excited to welcome the Cochran family to Athens."
Crimson Tide coach Nick Saban said Cochran had been "looking for a new career path."
"He wanted to get on to the field coaching and would like one day, I think, to be a head coach," Saban told ESPN. "We didn't really have anything here to offer him along those lines, and Georgia did. I understand him wanting to take on that path.
"As good as Scott was for us here as our head strength coach, it's probably best for him and best for us if he's able to do there at Georgia what he wants to do now with his career."
When Lane Kiffin was named the Ole Miss head coach, Kiffin expressed interest in hiring Cochran as an on-the-field coach.
Cochran and Smart shared a close relationship when Smart was the defensive coordinator at Alabama, and they have remained close over the years.
Cochran was the fifth-highest paid strength and conditioning coach in the FBS last season, earning $595,000 annually with potential bonuses of $130,900.
Smart tried to hire Cochran as his strength and conditioning coach when he was hired to coach the Bulldogs in 2016. Cochran now replaces Scott Fountain, who left to join Sam Pittman's staff at Arkansas.
Cochran was on Saban's staff for all six of his national championships, as Cochran served as an assistant at LSU in 2003.
Cochran and head athletic trainer Jeff Allen were the only two football staff members remaining who came with Saban to Alabama in 2007.
Saban noted that Alabama's new sports science center is scheduled to open this fall.
"We're in a good position to bring in somebody at the top of their profession, and I think we'll have a lot of people interested," Saban told ESPN. "I'm excited to see who all is out there."
ESPN's Mark Schlabach contributed to this report.