Stumpf will give up about 910,000 shares in unvested stock awards, and will not get a bonus this year, according to a statement released late Tuesday by members of Wells Fargo's board of directors.
Carrie Tolstedt, the executive in charge of the division where much of the activity took place, will give up about $19 million worth of stock.
Also, Wells Fargo's board announced it has hired a law firm to investigate the bank's sales practices. Stumpf, the chairman of the board, will recuse himself from matters related to the investigation, according to the statement.
Steven Sanger, Wells Fargo's lead independent director, said members of the board are "deeply concerned" about the bank's practices and will conduct its investigation "with the diligence it deserves."
Sanger also said the investigation could lead to more executives losing stock awards or even other compensation already paid.
"The independent members of the board will take such other actions as they collectively deem appropriate," he said.
The decision by the board comes two days before Stumpf is expected to appear before the House Financial Services Committee.
Stumpf came under heavy criticism last week when he was grilled by the Senate Banking Committee. The San Francisco banking giant has acknowledged that thousands of bank workers opened as many as 2 million checking, saving and credit card accounts for customers without their knowledge.
The bank has agreed to pay $185 million to federal regulators and the Los Angeles City Attorney's office over the fake accounts, a practice regulators say was encouraged by an aggressive and poorly supervised sales culture.
Federal prosecutors are investigating the bank to see whether criminal charges should be filed, and the Labor Department said Tuesday that it is investigating possible labor law violations. Meanwhile, the company is facing a mounting number of lawsuits from customers, employees and shareholders, including prospective class actions seeking billions of dollars in damages.
At last week's hearings, Sen. Elizabeth Warren (D-Mass.) called on Stumpf to step down.
"You should resign," Warren said. "You should give back the money you took while this scam was going on, and you should be criminally investigated by the Department of Justice and the Securities and Exchange Commission."
Warren and other senators pushed Stumpf to commit to giving back some of his pay and to claw back pay from Tolstedt.
Warren said on Wednesday that she was not satisfied with Wells Fargo's "small step in the right direction" because it was "nowhere near real accountability."
"Wells employees who failed to meet management's outrageous sales goals were fired," she said. "But John Stumpf is going to be just fine: He keeps his job and most of the millions of dollars he made while this massive fraud went on right under his nose.
She said Stumpf should resign.
"We still don't know how many customers were harmed and how long this fraud continued. We also don't know how many low-paid employees got fired for failing to meet quotas that Wells Fargo now recognizes were too high," he said.
According to Tuesday's announcement, Stumpf and the board reached a deal that calls for him to give up all of his unvested stock awards, which the company values at about $41 million, based on the $45.09 closing price of Wells Fargo shares Tuesday.
Unvested awards are those that have been granted but are paid out only after certain conditions are met, typically based on tenure and financial performance.
Stumpf will also not receive an annual bonus which, in the past, has totaled $4 million each year.
He will give up his $2.8 million annual salary during the investigation, which will cost him about $54,000 per week.
Also, Tolstedt, who announced her retirement this summer and was expected to stay with the bank through the end of the year, has left the company, the release said.
The board noted in its statement Tuesday that the actions against Tolstedt and Stumpf "will not preclude additional steps being taken" against them "or other executives as a consequence of the information developed in the investigation."
The two executives are giving up only unvested stock awards. They each own millions of dollars worth of Wells Fargo stock outright, and Tuesday's agreement does not call for the executives to lose any of that.
Tolstedt's holdings, including stock and vested stock options, amount to about $77 million. Stumpf's holdings add up to $109 million in stock, plus more than $24 million in accumulated pension and 401(k) benefits.
Jon Lukomnik, executive director of the corporate governance nonprofit Investor Responsibility Research Center Institute, said the board had little choice but to take back some pay.
Wells Fargo company policy allows the bank to revoke unvested awards from executives who are negligent or whose actions harm the bank's reputation. If the board had not revoked some pay, Lukomnik said it could have given investors grounds to sue the board.
Earlier Tuesday, the Labor Department said it had launched a "top-to-bottom review" of how Wells Fargo treated employees as it pushed the aggressive sales quotas.
A department working group has been established to review complaints alleging failure to pay overtime and other infractions, Labor Secretary Tom Perez said.
The agency also set up a special website for current and former Wells Fargo employees to instruct them how to file complaints about labor law violations.
Warren and other senators wrote to Perez last week asking for the probe. The senators noted several civil lawsuits and other complaints by Wells Fargo workers alleging the bank failed to pay overtime for late nights and weekends spent working to meet sales quotas.
The department has received whistle-blower program complaints from Wells Fargo employees over the last five years, Perez said. The majority of cases have been concluded "through settlement or other actions" and some were determined to have no merit. But the department will now go back and review all open and closed cases against Wells Fargo since 2010.
Warren said she welcomed the Labor Department review but added it should be broadened.
“Every other federal agency with jurisdiction in this matter should follow
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8:10 a.m. Sept. 28: This article was updated with comments from Sen. Elizabeth Warren.
7:20 p.m.: This article was updated with a comment from the board, details about the Labor Department investigation and other details.
5:35 p.m.: This article was updated with additional details and background.
5 p.m.: This article was updated with additional details and background.