Blood Red Shoes and The Kooks have also been newly confirmed for the two site event.
Sigur Rós have announced new album Kvekur, which will be released this June 17.
It's the band's first album since signing to XL Recordings worldwide.
The band have also unveiled aggressive new song Brennisteinn.
Meanwhile, Sigur Rós will play a series of European dates in November, including their biggest ever UK headline show at Wembley Arena on Thursday November 21.
Sigur Rós UK Headline Shows:
Nov 16 - O2 Arena, Dublin
Nov 19 - Nottingham Arena
Nov 20 - Brighton Centre
Nov 21 - Wembley Arena
Tickets go on general sale on March 28.