Sadiq Khan claimed expanding the West Sussex airport was "the only option that can actually be delivered".
His letter to Theresa May was signed by 30 cross-party London MPs, council leaders and London Assembly members.
It claimed a second runway at Gatwick would be the "obvious choice" for the capital and Britain.
"Gatwick would not only require no public subsidy - a huge factor in our current uncertain economic times - but would give Britain all the benefits of expansion whilst keeping our air quality safe and within legal limits," Mr Khan said.
In her keynote address to the Conservative Party conference in Birmingham, Mrs May confirmed that the government would "shortly announce" which airport would get the go-ahead.
The shortlisted options being considered are a third runway at Heathrow, extending its existing northern runway and a second runway at Gatwick.

Molinari stormed into contention with two eagles in the last seven holes to set a clubhouse target of nine under par, which Dunne was able to match thanks to a birdie on the last.
The players then returned to the 18th hole for a sudden death play-off.
A scrappy par proved to be enough for Molinari to secure the title.
Dunne, who had enjoyed a two-shot lead going into the final round, found trouble off the tee and failed to get up and down from a greenside bunker.
The 24-year-old's second place finish was his best ever on the European Tour however.
"I felt like there were just so many shots that slipped away from me. It's just one of those days," said Dunne.
"I felt like I was really close to shooting four or five under and stuck with one under in the end. I'm happy with my form and looking forward to next week.
"I'm just a bit disappointed not to come out with the result we wanted but it's a step in the right direction."
For the Italian, it was his first European Tour success since 2010.
The mayor of London has written to the prime minister in a last-ditch plea for an extra runway to be built at Gatwick Airport, rather than at Heathrow.
[NEXT_CONCEPT]
Ireland's Paul Dunne lost to Italian Edoardo Molinari in a play-off at the Trophee Hassan II at Royal Golf Dar Es Salam in Morocco on Sunday.