Chevron said on Oct. 3 that it supported Stumpf despite concerns about his leadership at Wells Fargo.
Target did not give a reason for Stumpf's resignation.
Stumpf joined the boards of Chevron and Target (tgt) in 2010.
Stumpf, who notified the companies' boards on Monday that he intends to resign, still serves on the board of Financial Services Roundtable, an advocacy group for the U.S. financial industry.
Stumpf's fall from grace started with a $185 million regulatory settlement among the bank, regulatory authorities and a Los Angeles prosecutor over its staff opening as many as 2 million accounts without customers' knowledge.
The misconduct, carried out by low-level branch staff to meet internal sales targets, shattered the bank's image and a raft of federal and state investigations followed.