The Metropolitan Police has made an "unreserved apology" to seven women deceived into relationships with undercover officers.
The apology and an agreement to pay compensation covers sexual relationships conducted by five officers from two undercover units.
They took place over 25 years until the units were disbanded in 2008 and 2011. One of the officers fathered children.
The women said the apology would "never make up for what we have endured".
Speaking on behalf of all seven women on Friday, two, Helen Steel and Belinda Harvey, said they expected more undercover relationships to come to light.
The other women's identities are protected and they are known as Rosa, Naomi, Lisa, Alison and Ruth.
The unprecedented, undisclosed financial settlements relate to officers who worked undercover for the Special Demonstration Squad (SDS), part of the Metropolitan Police and shut down in 2008, and the separate National Public Order Intelligence Unit (NPOIU).
Both teams deployed officers on long-term undercover operations to infiltrate radical political or social causes, such as environmental campaigns, anarchy and animal rights.
The longest relationship lasted for nine years.
Five former undercover officers, including Bob Lambert and Jim Boyling from the Met and Mark Kennedy of the NPOIU, were involved. These three are said by lawyers to have had more than one undercover relationship.
Mr Lambert's relationship with a woman called Jacqui led to the birth of a child. That case was separately settled last year for more than £400,000.
The two other officers were known by their targets as "Mark Cassidy" and "John Barker", but were named in Parliament as Mark Jenner and John Dines.
In each case the officers eventually disappeared, leaving their partners searching for years for answers.
In a statement on Friday, Assistant Commissioner Martin Hewitt said the relationships had been "wrong".
He warned any future officer who had a sexual relationship with someone they were targeting risked prosecution.
Asst Comm Hewitt said the women had suffered a violation of their rights, abuse of police power and significant trauma.
"Thanks in large part to the courage and tenacity of these women... it has become apparent that some officers entered into long-term intimate sexual relationships which were abusive, deceitful, manipulative and wrong," he said.
"These should never have happened. They were a gross violation of personal dignity and integrity.
"They were deceived - pure and simple. Whether or not genuine feelings were involved on the part of any officers is entirely irrelevant and does not make the conduct acceptable."
He said the relationships may well have reflected attitudes towards women that should have no part in police culture.
And he admitted that there had been no proper management of the deployments, even after the introduction 15 years ago of supposedly stringent legal controls.
The women said they were pleased that after a four-year legal battle the Met Police had recognised the "state sponsored, deceptive relationships".
"We have worked together on this painful and deeply personal legal case in order to expose the serious and systemic abuse of power by undercover police officers and their managers," they said.
"Although no amount of 'sorry', or financial compensation, can make up for what we and others have endured, we are pleased the police have been forced to acknowledge the abusive nature of these relationships and that they should never happen."
They said the cases showed a pattern of discriminatory behaviour towards women amounting to "institutional sexism".
And they criticised the police for failing to apologise to the children involved.
One of the women, known as Ruth, said she was still struggling to come to terms with her undercover relationship with Jim Boyling. Another, Rosa, said she thought he was her life partner and father of her children but he was "a fiction".
Alison met Mark Jenner when she was working to expose police corruption. She said, "I loved him very deeply."
Lisa's six-year relationship with Mark Kennedy had him attending her father's funeral - "a deception perpetrated by the state," she said.
The group are supporting another woman, Kate Wilson, who will pursue her case in court.
They said they believed such relationships were "widespread", and called on the police to reveal more officers' cover names.
The Metropolitan Police is still facing further claims and an internal police inquiry. Separately, a judge-led public inquiry is beginning to gather evidence as to what happened within the two units.