Greek Orthodox music will also be played as a tribute to his late father, Prince Philip the Duke of Edinburgh, who was born in Greece, into the Greek and Danish royal families.
It will be performed by the Byzantine Chant Ensemble.
Lord Lloyd-Webber, who is known for hit musicals including The Phantom Of The Opera, Evita and Jesus Christ Superstar, described himself as 'incredibly honoured' to have been asked to compose a new anthem.
A Coronation March has been created by Patrick Doyle, while a piece by Iain Farrington for the solo organ takes in musical themes from countries across the Commonwealth.
There will also be new works by Sarah Class, Nigel Hess, Paul Mealor, Tarik O'Regan, Roxanna Panufnik, Shirley J Thompson, Judith Weir, Roderick Williams, and Debbie Wiseman.
A handpicked gospel choir - The Ascension Choir - will perform as part of the service, as will the Choir of Westminster Abbey and the Choir of His Majesty's Chapel Royal, St James's Palace - together with girl choristers from the Chapel Choir of Methodist College, Belfast, and from Truro Cathedral Choir.
The King's Scholars of Westminster School will proclaim the traditional 'Vivat' acclamations. Bass-baritone Sir Bryn Terfel along with soprano Pretty Yende and baritone Roderick Williams will be among the soloists.