The festival, which will take place in four locations around the UK, is the most ambitious music event will be staged.
More than 175,000 tickets will be available to the event, costing just £18, plus a £4.50 booking fee.
Other acts on the line-up include Manic Street Preachers and Beck.
Each of the music radio stations will take part, with stages set up around the UK.
Radio 1, 1Xtra and Asian Network will take over Singleton Park in Swansea, Wales for the weekend, with Sheeran and Swift the headline acts.
Scone Palace in Perth, Scotland; and the War Memorial Park in Coventry, England will play host to Radio 2 and Radio 3, whose artists include Noel Gallagher, Nigel Kennedy, Billy Ocean and Snow Patrol.
And 6 Music will jet to Belfast, Northern Ireland, where the Titanic Slipways will see gigs by Beck, Courtney Barnett, Manic Street Preachers and Public Service Broadcasting.
Many more acts will be announced over the coming weeks, with the festival taking place from Friday 25 to Monday 28 May.
“You know it’s the start of the summer when we put on a massive festival, and we’re bringing two of the biggest artists in the world to Swansea,” said Radio 1’s Nick Grimshaw. “Taylor and Ed plus a whole massive line-up to be announced make The Biggest Weekend the event of the year.”
Chris Evans said to a presenter said: “The Biggest Weekend is shaping up very nicely indeed. Can’t wait to find out who else is going to be performing.”
The one-off event, which takes place during one of Glastonbury’s fallow years, will be covered extensively on BBC TV and radio, with full sets available on BBC iPlayer.
Tickets go on sale on Monday, 12 February. A set percentage of tickets will allocated to people living in each of the local areas.>