Wells Fargo’s chairman and its chief executive bought more than $5 million of the bank’s stock as they scramble to recover from a fake-accounts scandal that has left the bank’s reputation in tatters.

Wells Chairman Stephen Sanger purchased $3 million worth of Wells shares, and CEO Tim Sloan bought an additional $2 million worth, the company reported in regulatory filings Monday.

The stock buys, which came a week after the bank released a report absolving its current board of most of the blame for last year’s scandal, is a message to shareholders that “there’s nothing there that they know of,” Marty Mosby, analyst at Vining Sparks, told The Post.

It’s also a way for Sanger, whose seat on the board is being targeted by proxy advisers, to save his neck.

On April 25, Wells is scheduled to have its first annual shareholder meeting since the bank paid $185 million to settle with government agencies over a years-long scandal in which bankers would open fake accounts and credit cards in customers’ names to boost sales metrics.

The scandal led to the ouster of John Stumpf, the previous Wells CEO, and Carrie Tolstedt, the former head of retail banking, as well as a claw-back of $75 million in compensation.

Earlier this month, Institutional Shareholder Services recommended that investors give 80 percent of the 15-person board the boot, which would leave only Sloan and two directors who came on this year.

The bank has pushed back against ISS’ recommendations, and put out its own report blaming Stumpf and Tolstedt for the fake-accounts scandal.

While the board is likely to get an earful from investors, analysts told The Post last week they don’t expect any board members to lose their jobs.

This isn’t the first time that top company brass have tried to reverse a stock slide with their own wallets.

Last year, JPMorgan Chase CEO Jamie Dimon bought $26.6 million in his own company’s shares following a decline in the bank’s share price last February, a purchase that was the start of a 13-month bull run for the largest US bank.

“This would be reminiscent what we saw Jamie Dimon do this time last year,” Mosby noted.

Dimon’s stock purchase sent JPMorgan shares up 8.3 percent on Feb. 12 last year — the day the purchase was announced. The buys by Sloan and Sanger boosted Wells shares 2.7 percent, to $52.72.

Dimon also wasn’t desperately trying to regain confidence from his customers after ripping them off for years.