The 33-year-old has enjoyed a 15-year career in the game, and has been a popular figure at Castleford, Wigan, Hull FC, Bradford and Salford, as well as at Dewsbury.
“While I’ve enjoyed it here, it has been frustrating as well,” Godwin told the Rams’ official website.
“I’ve struggled with the transition to part-time rugby and picked up a few too many injuries along the way as well.
“I don’t think I’ve been able to play at my best over the last two years but it’s a busy and exciting time for me going forward.
“I’m working for a haulage company, I’ve just started university and me and my wife are looking forward to bringing our son, Charlie up as well.
“It’s a shame I couldn’t end my career the way I wanted to but I’ll always remember my time at Dewsbury and I’d definitely recommend the club to anyone out there who is looking for somewhere to play.
“I know there’s been a few, but I’d like thank every club I’ve played for.
“I can honestly say it’s been an honour to wear every single shirt. I’ve played with some ‘legend’ blokes and in front of some fantastic fans and I’m so lucky to have made many friends along the way.
“I’m looking forward to the next chapter, and hopefully I’ll still be involved in Rugby League, as it’s the greatest game of all.”
Dewsbury coach Glenn Morrison, who played alongside Godwin at Bradford, paid tribute to a player with whom he loved working.
“He’s one of those people you can’t help but like and it’s been a pleasure to coach him,” he said.
“Every player he’s ever played with is his best mate. He’s a great bloke and I know he hasn’t been able to get the best out of himself at the Rams but, all the time he hasn’t been playing, he’s been giving his all for the club.
“He’s always wishing the boys the best and supporting us and I know that won’t change in the future.
“He’s had a great career and should be proud of what he’s achieved and, this weekend, at our last home league game, Wagga’s going to have his final walk on the pitch and have a final farewell to his playing days.
“Hopefully we can get as many supporters as possible from all the clubs he’s been at to help give him a farewell to the sport the way it should have been.”