The Manchester band play the outdoor stage near the iconic Lovell telescope in Cheshire on June 23. Weller plays the following day. Both artists will be supported by special guests.
"As well as providing an amazing backdrop the telescope will also be serving a secondary purpose as the world's most incredible projection screen," organisers said.
"Throughout the day there will be experiments and workshops along with free access to the new visitor centre - but come evening it's all about the music and one mind-blowing and totally unique show."
Tickets go on sale this Friday, March 1 at 9am and are priced at £35 per day.
Last year saw a show at the scientific landmark in Lower Withington, Cheshire, featuring the Flaming Lips, British Sea Power, OK Go and Alice Gold.
Watch the Flaming Lips perform 'Race For The Prize' at Jodrell Bank last year below: