The New York band are known for their flamboyant style

Tickets for the show, on 16 September, will be allocated through a prize draw, which can be entered online or by text.

"Scissor Sisters have called all of their surviving grandparents to gush with excitement," songwriter Babydaddy said in a statement.

The gig is being held in support of the Global Fund, which provides money to fight Aids, tuberculosis and malaria.

It will be held from 1800 BST in the square, which has previously seen concerts by the Pet Shop Boys and REM.

Scissor Sisters are relatively unknown in their native US, but their first album went to number one in the UK, and won three prizes at the 2005 Brit Awards.

"London is our spiritual home, and the UK gave us our first and longest-lasting embrace," said Babydaddy.

The flamboyant New York band release their new album, Ta-Dah, two days after the Trafalgar Square concert.