The striker re-joined the Dens Park side on a loan deal from Celtic until the end of the season.
Griffiths had been linked with a return to Hibs, as well as a move to Aberdeen during the transfer window.
The 31-year-old signed a one-year extension to his Celtic deal this summer but has not featured under Ange Postecoglou, making the bench just twice.
The influence of manager James McPake was key, having been a team-mate at both Hibs and Livingston.
“James picked up the phone and made me feel wanted. That was a big factor for me, I’ve known him my full career and looking forward to playing with him.
“My goal record speaks for itself and that’s what I come here to do. I’ve come here to score goals and make sure Dundee stay in the league.
“I’m sick of saying I have points to prove. I’m just going to let my football do the talking, help the team, make sure we are up that table, score goals and make sure I’m playing well.”
McPake revealed that the move was in doubt on Monday when another club entered the frame, but the Dundee boss is ecstatic he was able to add someone of Griffiths’ calibre.
The striker has nearly 250 career goals, including 33 goals in 62 appearances in his first stint at Dundee, which included helping the team win the Challenge Cup.
“He's a proven goal scorer at every level he's played at," he said.
“Goals, Leigh Griffiths brings that. His hold up play, all-round play has developed since he was a kid at Livingston.
"When you get a player like Leigh Griffiths to a club like Dundee, you are going to try and do all you can to get him here. We worked really hard. It was in doubt last night with another club in for him but we’re delighted he’s chosen here.”