The 31-year-old goalkeeper was stopped by a routine patrol in Gloucester Place in the early hours of Friday.
Lloris has been at Spurs since joining from Lyon in 2012, making 256 appearances for the Premier League club.
The Frenchman has "wholeheartedly" apologised for the incident saying it was "completely unacceptable".
"I wish to apologise wholeheartedly to my family, the club, my team-mates, the manager and all of the supporters," said Lloris.
"I take full responsibility for my actions and it is not the example I wish to set."
Lloris captained France as they won the World Cup for the second time in Russia this summer.
The Metropolitan Police said Lloris had been released on bail and was due at Westminster Magistrates' Court on Tuesday, 11 September.
Tottenham have started the Premier League season with a 2-1 win at Newcastle and a 3-1 home victory over Fulham.
Their next match is at Manchester United on Monday (20:00 BST kick-off).