In a statement, Scotland Yard also said an out-of-court settlement had been reached with the family of the newspaper vendor, Ian Tomlinson, the London Evening Standard reported.
The widow, Julie Tomlinson, said the apology and settlement was "as close as we are going to get to justice."
Tomlinson died April 1, 2009, after he was struck with a baton and pushed to the ground by Metropolitan Police Constable Simon Harwood as he walked home.
An initial autopsy determined Tomlinson died of a heart attack. Two successive post-mortems ruled he died of abdominal bleeding caused by a blow.
A May 2011 inquest found Tomlinson was illegally killed and Harwood was charged with manslaughter. The officer was acquitted in July 2012, but fired two months later for gross misconduct.
"I apologize unreservedly for Simon Harwood's use of excessive and unlawful force, which caused Mr. Tomlinson's death, and for the suffering and distress caused to his family as a result," Met deputy assistant commissioner Maxine de Brunner said.
De Brunner also apologized for "ill-considered comments" to the media after Tomlinson's death, "significant failings" in vetting Harwood for his position, failing to inform the family of the officer's contact with the deceased before they learned of it in the media and for inaccurate information given by a police officer to pathologists investigating the death.
The amount of the financial settlement was not released.