The Scotland international appeared to be in his final few months at Parkhead after previous manager Ronny Deila revealed he had rejected a new contract towards the end of last season
But he has looked rejuvenated in recent games under Rodgers and Celtic have announced he has committed his future to the club until 2019.
The winger has featured in all five competitive matches this season and scored in Sunday's 2-1 victory over Hearts at Tynecastle.
Forrest, whose previous contract was due to expire at the end of December, told the club's official website: "From day one it's been really positive and the manager's had a good impact on all the boys and I think it's shown in a lot of our good performances so far
Hopefully, as time goes on we kick on and do even better.
"I had a chat with the manager in the off-season and as soon as we came back in pre-season, and he just said, 'show me what you've got.' I made it clear that I wanted to stay here and I'm just glad it's done now and I can focus on playing.
"I've been here since I've been nine
It's all I know and it's a massive club - one of the biggest in the world - so I'm just delighted to sign here again."
Forrest broke the 30-game barrier for the first time in four years last season after Deila and his sports science staff worked hard to get the player consistently fit after a series of muscle injuries hindered his progress, but he became a more peripheral figure as the campaign drew to a close
However, with Rodgers' backing and a new deal, Forrest is looking to build on his 31 goals and 193 appearances for the club.
The Prestwick-born player, who made a goalscoring debut against Motherwell in May 2010, added: "I feel that I've got a bit of experience now and I just want to kick on and just play as many games as I can for this club
"We've made a few signings and they've made a good impact and it's good for the squad, and we've also put in a couple of good performances against Astana to get to the play-off round, so it would be great to get into the group stages of the Champions League this season."
Source : PA
Source: PA