The Elbow gig will take place on 26 May and will be broadcast on Absolute Radio on 5 June from 7pm to 8pm. The recording will be repeated on Absolute Radio's digital station Absolute Radio 00s.
Absolute Radio will be recording and streaming Elbow in Fully Lossless Audio Codec (or FLAC) technology, known as full high definition audio, which a spokeswoman said will provide a superior audio experience for fans.
Clive Dickens, chief operating officer at Absolute Radio, said: "We're passionate about live music and are using Absolute Radio's digital expertise to bring our listeners even closer to the performances in 2011.
"Elbow are a hugely popular band amongst our audiences and we are incredibly proud they are kicking off Absolute Radio Live - to do it in such a memorable setting as St Paul's Cathedral will make it all the more special."
Absolute Radio's summer line-up of events includes The Isle of Wight Festival, Hard Rock Calling, the 80s Rewind Festival, Pulp at the Wireless Festival and two Kings of Leon gigs from Hyde Park.
The radio station has severed commercial ties to the V Festival but still has editorial interests in this year's event.
Last month, insurance brand Swiftcover.com renewed its sponsorship of Absolute Radio Live in a deal which will see the station stage a festival in a listener's garden and the brand sponsoring Absolute Radio's version of the Radioplayer.