In doing so, the Aviva Premiership club have ended growing speculation about McGeechan's future. His existing two-year contract ends next month.
Bath have suffered an erratic season, finding themselves well adrift of the Premiership play-off race and struggling to secure automatic qualification for next season's Heineken Cup.
McGeechan's exit, which coincides with the end of an existing two-year contract, will spark a coaching reshuffle.
Press Association Sport has learnt that Bath forwards coach Martin Haag is also set to depart, although the club's current skills and defence specialist Brad Davis could remain.
South African Gary Gold and Australian Michael Cheika are believed to be the top two contenders to become head coach of the club.
It is also believed that Nick Mallett, who was recently beaten to the role of England boss by Stuart Lancaster, is not being considered by Recreation Ground chiefs.
Bath say they are making "good progress" in identifying a head coach, claiming a new structure and coaches will be agreed and in place during the summer in readiness for next season.
McGeechan, 65, initially joined Bath as performance director. He held previous coaching roles with Northampton and Wasps, and is synonymous with the British and Irish Lions, having headed up four tours during a 20-year spell.
Bath chief executive Nick Blofeld said: "We would like to thank 'Geech' for his time with the club and for his assistance in developing the culture at the club through this transitional period.
"An announcement regarding a new head coach will be made in due course."
Gold is currently in temporary charge of Premiership relegation favourites Newcastle, while Cheika is at French club Stade Francais.