The new show follows episodes featuring Noel Gallagher, Dave Grohl, Kylie Minogue, and Rod Stewart.
The track features a backing band made up of Ed Sheeran, Griff, Lewis Capaldi, Sam Smith and Yungblud.
Walker and Badu are known to be fans of each other’s music, with Walker noting she grew up on Badu’s highly acclaimed work from the 90s.
The track also features on the 20th anniversary edition of ‘The Invisible Band’, out on December 3.
The acts came together for the special version at BBC Radio 1’s Out Out! Live 2021 event at London’s O2 Arena.
The song was a feature of Taylor's, first, self-titled album, his only release for the Apple label in 1968.
Watch BBC documentary on the exceptionally gifted musical family the Kanneh-Masons, ‘Imagine: This House Is Full Of Music’, on 29 August 2021.
Eilish was joined by her brother Finneas on acoustic guitar for the stripped back, mellow rendition of the track.
The session includes a cover of Puff Daddy and Faith Evans’ ‘I’ll Be Missing You.’
The program is set to be broadcast on Saturday, July 31, on BBC One at 10.30pm UK time.
Subject to UK government guidelines, this year's event will this year be held at the Eventim Apollo in London on September 9.
The ambitious live-streamed event on May 22 will also feature Damon Albarn, IDLES, Jorja Smith and many more.
‘Britain has produced a lot of brilliant female singer-songwriters and vocalists, but there was only ever one Amy Winehouse.’
Set to take place over the weekend of March 26-28, this year’s festival will be digital only due to the COVID-19 pandemic.
The new clip is on the revered singer-songwriter's YouTube channel, along with each of the individual songs in the set.