Davies, who had been Jenkins' closest rival for the national job, returns to Stradey Park after spending 10 years in charge of Leeds.
"I spent all my playing days at Llanelli and it's always been close to my heart," said Davies, who has signed a three-year contract.
"Once you've played for the Scarlets, it's stays with you for life. It's a great place with lots of tradition and it was an easy decision to come back."
Davies quit Leeds after they were relegated from the Guinness Premiership this season but he believes his coaching experience at Headingley stands him in good stead.
He joined Leeds from the Scarlets as player-coach and helped guide the club from National Division Three into the top flight inside five years and they won last year's Powergen Cup at Twickenham.
"I've had a great experience in Leeds and really enjoyed it. I've gone through varying periods of having to build a team to go into different competitions," said Davies.
"In terms of learning, I think you continue to learn as long as you live. Coaching goes through stages and this is another stage in my development."
The former Llanelli number eight, who won 46 caps for Wales, was chosen from a short-list of six candidates.
"I'm confident I've got the right man," said Scarlets chief executive Stuart Gallagher.
"I've deliberately taken my time, spoken to people whose opinion I respect because I wanted to make certain that the next guy is the right guy."
Jenkins took assistant coach Nigel Davies with him into the Wales set-up and Davies will appoint a new coaching team at Llanelli in due course.