The 42-year-old won 14 caps for Great Britain and played three times for England in a professional career that started at Wigan and also saw him play for Leeds Rhinos, Bradford Bulls and Warrington Wolves. In 1997, he was named in the Super League Dream Team.
Forshaw had a brief rugby union stint as a player at Saracens and was briefly the player performance advisor for the Rugby Football League.
He served a number of years as assistant coach with Wigan Warriors before coming to Connacht.
Commenting on Forshaw's departure, the province's head coach Eric Elwood said: "When I took the job as director of rugby, I wanted to appoint a defensive coach because I felt this was crucial for us to progress and move forward as an organisation.
"The key when hiring people is that they are a good person and a good fit for your organisation and we got the right person in Mike.
"One of Mike's strengths was his technical work in both the tackle and wrestle areas. We found this hugely beneficial, particularly in the off-season. He is a fantastic motivator and always got the best out of players.
"We want to thank Mike for all the good work he's done for Connacht Rugby over the last three years. We wish him every success for the future in whatever path he takes. We have nothing but praise for Mike and wish him well in the future."
Forshaw himself said: "I'd like to thank Eric (Elwood) for giving me the opportunity to work with Connacht Rugby for the last three years.
"I also have to credit the players on their outstanding work ethic. I have nothing but praise for the way they've responded to me from day one.
"I've enjoyed my time immensely at Connacht Rugby and I believe that there is now a real culture and sense of pride with regards to the team's defence. It means something to them and is a big part of how they want to play.
"I'm looking forward to the next challenge in my career and hopefully building on my experiences that Connacht has provided me."