Forwards Coach Carl Hogg will take charge of preparations for the home fixture with Sale Sharks on Saturday.
The 40 year old Scot took over as Head Coach of Gloucester Rugby ahead of the 2009-10 season, having previously served as the club's backs coach following a glittering playing career which included representing Scotland at two Rugby World Cups.
In his first season at the helm, he guided Gloucester to a seventh place finish in the Guinness Premiership.
In 2010-11, the club won the LV= Cup, finished third in the Aviva Premiership and only lost a semi final play off to eventual winners Saracens by two points.
However, 2011-12 has been more of a struggle with the team losing a number of close fought games to late scores.
With just two matches remaining this season, Redpath has now taken the decision to end his three year tenure.
"It's a result driven business we're in and I hold my hand up and take full responsibility for the fact that we've not performed as well as we should have.
"I've offered my resignation with a heavy heart. I have dearly loved my time at Gloucester. It's a fantastic club in a true rugby city with devoted, passionate supporters. But, I think it's now someone else's turn to take charge.
"There are a lot of people to thank, too many for a press release. However, I must express my gratitude to the Walkinshaw family, Ryan and his father Tom before him, for giving me such a marvelous opportunity here.
"I genuinely think that the future for Gloucester Rugby is bright and I sincerely wish everyone connected with the club the very best for the future."
Gloucester Rugby Board Member Ryan Walkinshaw admitted that it's a sad day for the club.
"It is with great sadness that the board accepted Bryan's resignation. He's a fine man, a good coach with strong principles and no-one could have worked harder to make a success of the role.
"However, he feels responsible for the recent run of disappointing results on the field of play and feels that he has taken things as far as he can. We respect that decision.
"We would like to stress that Bryan's departure is not connected with recent media speculation regarding his future and is based purely on results.
"We would like to thank him for everything he's done for Gloucester Rugby and wish him every success in his future endeavours."