Mr Khan is the city's first Muslim mayor, after beating Tory Zac Goldsmith by 1,310,143 votes to 994,614.
The result bolsters leader Jeremy Corbyn after Labour was beaten into third in Scotland by the Tories and lost some English councillors.
In Scotland, the SNP said it would form a minority government after winning its third election in a row.
First Minister Nicola Sturgeon is celebrating what she said was an "emphatic" victory, her first as party leader, after the SNP emerged as the largest party at Holyrood with 63 seats, ahead of the Conservatives on 31 and Labour on 24.
But she played down talk of another independence referendum after falling short by two seats of an overall majority.
In Wales, Labour remains as the largest party, with 29 out of 60 seats, but was denied a majority as Plaid Cymru and UKIP both made notable gains. Counting is continuing in Northern Ireland.
Sadiq Khan has been elected the new Mayor of London - boosting Labour after it slumped in Scotland's elections.