The King has personally chosen the music for the ceremony at Westminster Abbey on 6 May.
Lord Lloyd-Webber said he wanted his new coronation anthem to reflect a "joyful occasion".
A gospel choir will sing and there will be Greek Orthodox music in memory of the King's father, Prince Philip.
The music will have a traditional tone with pieces from classical composers such as William Byrd, George Handel and Sir Edward Elgar.
But there has been a coronation theme of combining the modern with the ancient - and new music has been commissioned.
This includes a coronation march from Patrick Doyle, who has previously written a different kind of royal music, with the award-winning soundtrack for Sir Kenneth Branagh's movie version of Shakespeare's Henry V.
It still remains uncertain who will be invited to listen to the music in person - in particular, whether Prince Harry and Meghan, the Duchess of Sussex, will be in the congregation.
Being crowned alongside the King will be Camilla, the Queen Consort, who earlier this week tested positive for Covid.
However, suggesting she was recovering, the 75-year-old Queen Consort is scheduled to be back carrying out engagements next week.
Camilla has avoided sensitivities about the crown she will be wearing, with the announcement last week that it would not include the Koh-i-Noor diamond, whose ownership has been disputed.
The new coronation music will include six pieces for orchestra, five choral works and a piece for the organ.
Lord Lloyd-Webber is writing an anthem based on the Biblical text of Psalm 98, that begins: "O sing unto the Lord a new song; for he hath done marvellous things."
The composer and theatre owner, aged 74 like the King, has had a long career writing popular musicals, such as The Phantom of the Opera and Cats.
Lord Lloyd-Webber, who retired from the House of Lords in 2017, has campaigned to support music and the arts.