Confirming the news to the Official Club Website, Haynes said: "I have been at Ipswich for six years so it's been a difficult decision to leave the Club but it's the right time in my career to move on.
"I want to thank the coaching staff and everyone at Ipswich for the help they have given me in my time there, especially the supporters who have been fantastic to me.
"Roy Keane has brought in some new players and has his own ideas on how he wants to take Ipswich forward and I respect that. It's important for me though to play regular first team football and I'm now looking forward to a new career at Bristol."
During his time at Town, Haynes was involved in 128 games for the club including 85 as a substitute scoring 19 goals since making his debut for the club in September 2005 against Leeds United as a substitute.