The Rovers wide man joined before last season's campaign and was Darrell Clarke's sixth signing of the summer.
Monkhouse, born in Leeds, began his career as a trainee with Rotherham United and went on to score nine goals in 128 league appearances for the Millers.
He joined Swindon Town in June 2006, but injury meant that he but only made 10 league appearances for the Robins and he spent time on loan at Hartlepool United before signing a permanent deal at the Victoria Ground in January 2007.
A member of the side that gained promotion to League One at the end of the 2006/07 campaign, he was also named in the PFA League Two Team of the Year that season.
Released by Hartlepool last summer he scored 44 goals in 290 league games for the club and appearances in other competitions took his total appearances to 322.
In Rovers promotion campaign, Monkhouse was ever present in Darrell Clarke's side making 42 appearances scoring 8 goals as Rovers returned to the Football League.
Season highlights for Monkhouse came in scoring the winner against Wrexham at the Mem, and hitting the back of the net in Rovers 4-0 win over Macclesfield, 5-1 win over Chester and 7-0 win over Alfreton on the final league fixture of the season.
On hearing Monkhouse's decision not to sign an extension with the club, manager Darrell Clarke told us "I am disappointed that Andy has decided to leave the club but I fully understand his reasons behind it.
"He has been a fantastic servant for us this season both on and off the field and he would be a great loss to any side.
"I want to wish him well in the future in finding a new club and I'm sure our paths will cross again."
Everyone at Bristol Rovers would like to wish Andy the best of luck ahead of the new season!