The Metropolitan Police (MeT) have also paid substantial, undisclosed amounts of compensation to the women who had relationships lasting up to nine years, leading to birth of a child in one case.
The apology comes four years after the women launched legal action against the police, alleging the deception caused them emotional trauma.
The case was settled out of court and as part of the settlement Martin Hewitt, an assistant commissioner at the Met Police,issued a statement saying: "Thanks in large part to the courage and tenacity of these women in bringing these matters to light it has become apparent that some officers, acting undercover whilst seeking to infiltrate protest groups, entered into long-term intimate sexual relationships with women which were abusive, deceitful, manipulative and wrong".
"I unreservedly apologise on behalf of the Metropolitan Police service. I am aware that money alone cannot compensate the loss of time, their hurt or the feelings of abuse caused by these relationships, Hewitt added.
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"Most importantly, relationships like these should never have happened. They were wrong and were a gross violation of personal dignity and integrity. The Metropolitan Police recognises that these cases demonstrate that there have been failures of supervision and management," he said.
Both teams deployed officers on long-term undercover operations to infiltrate radical political or social causes, such as environmental campaigns, anarchy and animal rights.
"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," the women said in a statement.
The settlements cover the actions of five former undercover officers, including Bob Lambert and Jim Boyling from the Met and Mark Kennedy of the NPOIU. These three are said by lawyers to have had more than one undercover relationship.