It comes after PC David Carrick pleaded guilty to 49 offences, including dozens of rapes.
Sir Mark Rowley announced all 45,000 Met officers and staff would be rechecked for previously missed offending.
He also apologised to Carrick's victims for the force's failings.
"We have failed. And I'm sorry. He should not have been a police officer," he said.
"This man abused women in the most disgusting manner. It is sickening. We've let women and girls down, and indeed we've let Londoners down. The women who suffered and survived this violence have been unimaginably brave and courageous in coming forward.
"I do understand also that this will lead to some women across London questioning whether they can trust the Met to keep them safe.
"We haven't applied the same sense of ruthlessness to guarding our own integrity that we routinely apply to confronting criminals."
The Met said a total of 1,633 cases of alleged sexual offences or domestic violence involving 1,071 officers and other staff were being reviewed from the last 10 years to make sure the appropriate decisions were made.
It can now be reported that Carrick had already pleaded guilty in December to 43 charges, including 20 counts of rape, and admitted the final six counts on Monday.
He committed the offences against 12 women across two decades.
The Met apologised after it emerged Carrick was brought to the attention of police over nine incidents including allegations of rape, domestic violence and harassment between 2000 and 2021.
Meeting some of the women on dating websites, he would control what they wore, what they ate, where they slept and he even stopped some of them from speaking to their own children.
It emerged he had been accused of two offences against a former partner the year before he passed vetting to join the Met in 2001, and faced further assault and harassment claims against an ex-girlfriend in 2002, while still in his probationary period.
Despite having five public complaints to his name, he passed checks to become a firearms officer when he transferred to the Parliamentary and Diplomatic Protection Command in 2009 and he was vetted again in 2017.
A spokesman for the prime minister said high-profile cases such as Carrick's had "shattered" the public's trust in policing.
Rishi Sunak retains faith in the Met and its chief Sir Mark Rowley, the spokesman said, adding: "The commissioner has acknowledged the significant work required by the force."
Baroness Casey, who is conducting a review of the force's standards and internal culture, called on the home secretary for a full inquiry into Carrick's case.
"We owe it to all of his victims that this work takes place," she said.
She added the scope of Lady Elish Angiolini's current non-statutory inquiry into the abduction, rape and murder of Sarah Everard should be extended to include the actions of Carrick.
Any inquiry into Carrick should "include the conduct of David Carrick and the potential opportunities the Met, other police forces and organisations may have had to identify his pattern of behaviour prior to October 2021, to stop him being a police officer and, ultimately, stop him offending," she said.
The issue was "so serious", she said, that if extending the current inquiry was not possible she would volunteer to conduct a separate inquiry.
Watch: We failed and let women down - Met police chief