Commissioner Cressida Dick said they were looking into "potential breaches of Covid-19 regulations" in Downing Street and Whitehall since 2020.
Boris Johnson told the Commons he welcomed the investigation as it would "give the public the clarity it needs" over the allegations.
His spokesman also said the PM did not believe he had broken the law.
Dame Cressida said the investigation was launched after the Cabinet Office inquiry team, led by civil servant Sue Gray, passed information to the force.
It remains unclear whether the Met probe will delay the publication of Ms Gray's report, which had been expected this week.
Earlier, the PM's spokesman said parts of her inquiry would not be published until after the police investigation is completed.
But Downing Street later said talks about what is "suitable to publish" were still ongoing.
BBC political editor Laura Kuenssberg said the Met seem to have no objection to the full report being published, meaning it may be published sooner rather than later.