The defender agreed terms on a one-year contract with Morton over the weekend and is excited to team up with his ex-Stirling gaffer Moore again.
Forsyth, 28, was handed offers from other clubs - including a new deal at Forthbank - but could not pass up the chance to sign for Moore.
Forsyth told the Tele: "That was probably a deciding factor. I had opportunities to go elsewhere, but the chance to work with Allan was key for me.
"He knows what I can do and I know the type of manager he is. We've got a good working relationship and I know I will enjoy working with him again.
"I know Allan and Mark McNally really well and know the training they do, and the type of football they play, so it was definitely a big thing for me to work with them again.
"It will help me settle in. I always thought training with Allan and 'Nally' was great and that's what you want.
"I've been speaking to the manager for a few weeks now, but I'm absolutely delighted to sign and I'm looking forward to next season."
With Forsyth settled in a career outside football, he has chosen to join on a part-time basis - but the full-back sees no reason why he cannot still be a hit.
He said: "I managed to balance that when playing with Stirling - it's just going to be the other way about, as I'll be training in the morning this time rather than at night.
"But I managed that last season so there is no reason why I can't balance the two again with Morton next year.
"I have another job but the club are being flexible and the manager is going to be flexible if I need to go to work.
"I work for a financial services company in Glasgow and will still be working there but will combine that with football as well."
The defender, who Moore signed for Stirling in 2005, is confident his new side can build on the progress made this season, and is aiming for a top-four finish.
Forsyth added: "Although they finished seventh, the last few games were disappointing results and arguably they should probably have finished in fourth or fifth position.
"I know the gaffer had targeted top six but talking the way he is, I don't see any reason why we can't be pushing for third or fourth place.
"I would like to see us pushing for that top four position."