Fifty-nine people were also injured when a lone male attacker detonated an explosive device at the end of a concert by Ariana Grande on Monday.
Commissioner Cressida Dick said the extra officers will be in place "for as long as it is needed".
She condemned the blast in Manchester as "an utterly appalling attack".
The mayor of London said Londoners would "see more police on our streets."
The capital has been on high alert since four people were killed in the Westminster terror attack two months ago.
Operation Hercules, which sees the deployment of a range of armed officers, is to be "stepped up... to make London as hostile an environment as possible for any would-be attacker", the Met said.
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Ms Dick, Britain's most senior police officer, said the extra armed and unarmed officers in London "are there to reassure".
"We are providing every possible support through the counter-terrorism network as investigators work tirelessly to understand what has happened," she said.
Mayor Sadiq Khan said London "stands united with the great city of Manchester".
He said he was "in constant contact with the Metropolitan Police, who are reviewing security arrangements in London".
"Manchester and the rest of Britain will never be cowed by terrorism," said Mr Khan.
Scotland Yard is currently reviewing "in detail" all upcoming events in London.
These include sports events at Wembley and Twickenham this weekend where armed officers will be deployed.
Commander Jane Connors said police "are determined to do all we can to protect the capital".
The Metropolitan Police has increased the number of officers on duty in London after the attack at Manchester Arena, which killed 22 people.