Brister, who joined Pinsents from Linklaters in October 1996, plans to focus on other interests including his holiday home rental company, Rural Retreats.
He will continue as a partner at Pinsents until the end of this year and then take on a consultancy role with the firm.
Pinsents has already elected to replace Brister with the firm's head of corporate Alan Greenough. He takes over the top spot in the London office on 1 May.
Brister's resignation comes as Pinsents continues it strategic review of the whole firm.
Brister was to have played a big part in implementing the changes stemming from the review but opted to resign now, knowing he would not be there to see the transformation through to the end