The 23-year-old midfielder played under the new Rovers boss at youth level, before moving to Selhurst Park after a successful loan spell.
Now reunited with Bowyer back at Ewood Park, Marrow hopes to help Rovers mount a push for promotion - just as he did with Palace last term.
"I'm obviously very happy to be back," said Marrow, who has signed a three-year deal with the club.
"I think when I left, it was probably the right thing to do at the time, because I didn't have the opportunities I was getting at Palace, but to come back is great.
"During the three years away, I think I've grown up a lot. I think I was a boy when I left and I'm just looking forward to getting back playing.
"Because I was here before, I think it was an easy decision. The facilities are first class and I know how good the club is, so it was a no brainer.
"Playing for Gary again was probably the biggest part. I knew how good a coach he was and how much I enjoyed playing for him last time, so that was a key thing.
"Hopefully it's a good time to come in and we can push on again and achieve something."
Marrow first joined the club in 2008 and played alongside the likes of Alan Judge, Grant Hanley, Jason Lowe and Josh Morris in Rovers' Reserves.
After gaining valuable experience of first team football on loan at Oldham and Crystal Palace, he made a permanent switch to Palace in January 2011.
Despite helping the Eagles secure promotion to the Premier League last season, Marrow had no hesitation in returning to his native North West.
"I learnt so much being here first time and I owe the club a lot for giving me my chance, because I started late at 18, so I'm looking forward to repaying a bit of that and obviously repaying the trust that Gaz has put in me by bringing me in," Marrow added.
"Palace was a big learning curve, obviously being away from home. It's one of those things that you look back on and you know you've done and it gives me a bit more experience, so I wouldn't change it, but I'm glad to be back up north to be honest.
"I didn't realise quite how many people I knew here. You forget. From the chefs to the receptionists and the kitman, and obviously seven or eight players, as well as Chris Taylor who I played with at Oldham, so it's been easy to settle in.
"I'll be looking to bring energy, commitment and hopefully get everyone going around me. If we can all pull together, on and off the pitch. We seem together and up for this season, so I think it's a good team to be in and around.
"We've got good depth to the squad and I think we've got a lot of quality as well, which you need in the Championship.
"Obviously at some point in my career it would be nice to play in the Premier League, but I think speaking to the gaffer and with everything here, it was quite an easy decision for me to come back to this club and play for him again and hopefully we can do the same as we did at Palace and push right on."