The Icelandic stars will also appear on 'The Tonight Show with Jimmy Fallon' (NBC) on 15 May
The London band released the special track last month after it debuted during Episode 2 of the hit show’s final season.
An array of stunning Rolling Stones collaborations finds a band that have forged their own unique path sharing the spotlight with fellow musical legends.
The song was aired in 'Game Of Thrones'' ‘A Knight of the Seven Kingdoms’ episode, which reportedly attracted 10.29 million viewers on its initial live broadcast on HBO.
Florence Welch says: "The magic and ritual in Game of Thrones, not to mention the costumes, have always appealed to me. I am honoured to be a part of the final season.”
The two artists are also co-headlining a US summer tour, also titled Night Running, with Spoon joining the bill for most of the dates.
The soul icon is due to perform what is billed as a “Celebration of Life, Love and Music” spanning his entire career.
The 36-track album features hits and key tracks from every studio album by the Stones from 1971 to date.
The festival returns to Ireland’s County Laois between 30 August and 1 September this year.
George Ezra also won Best British Male Artist, while Jorja Smith was awarded Best British Female Artist.
The band will be supported at different dates by Christine and the Queens, Blood Orange, Nathaniel Rateliff & the Night Sweats and others.
New single 'Moderation' was first premiered on the Australian leg of the band's 'High As Hope' tour. It's backed with a second new track, 'Haunted House'.
The band was recently nominated for various BRIT awards, alongside Florence + The Machine and Sam Smith.
Ariana Grande, Drake and Eminem are also in the running in the award ceremony's International categories.
Lil Wayne, The 1975, Kacey Musgraves and more also confirmed for the event.