The Swedish music stars will appear with the current London cast of the musical Mamma Mia! to celebrate its 15 years in the West End.
Hit musicals Charlie and the Chocolate Factory and Stephen Sondheim's Merrily We Roll Along are the most nominated shows, with seven nominations apiece.
Gemma Arterton and Stephen Mangan will co-host this year's ceremony.
The awards, the biggest event in the UK theatre calendar, will take place at the Royal Opera House in central London.
Dame Judi Dench, Lesley Manville, Jude Law, Rory Kinnear and Tom Hiddleston are among the acting nominees.
The best actor race includes three Shakespeare performances: Law's Henry V, Hiddleston's Coriolanus, and Kinnear for his role as Iago in Othello.
They are up against Henry Goodman for his role as a Hitler-like Chicago crime boss in The Resistible Rise of Arturo Ui.
Tenor Joseph Calleja and Broadway star Bernadette Peters will also performDame Judi, nominated for Peter and Alice, is up for best actress alongside Manville's turn in Ghosts, Hayley Atwell for The Pride and Anna Chancellor for Private Lives.
Women dominate the best director category, with Merrily We Roll Along's Maria Friedman, The Scottsboro Boys' Susan Stroman and Chimerica's Lyndsey Turner up against Ghosts director Sir Richard Eyre.
The best new comedy category returns for the first time since 2010 with The Duck House, The Full Monty, Jeeves and Wooster in Perfect Nonsense and The Same Deep Water As Me all in contention.
A week after its Olivier nomination in March, it was announced that The Full Monty would close in the West End after just five weeks due to poor ticket sales.
The show received strong reviews and had already completed a UK tour following its 2013 premiere in Sheffield.
The awards evening will feature performances from all four nominees in the best new musical category - The Book of Mormon, Charlie and the Chocolate Factory, The Scottsboro Boys and Once.
There will also be performances from all the BBC Radio 2 Audience Award nominees - Les Miserables, Matilda the Musical, The Phantom of the Opera and Wicked.
The awards are named after the actor knight and theatrical giant Lord OlivierBroadway star Bernadette Peters and opera tenor Joseph Calleja will also perform at the ceremony, highlights of which will be shown on ITV at 22:15 BST.
The success of musicals such as The Book of Mormon and Charlie and the Chocolate Factory led to record ticket sales for London's theatres last year.
Attendances were up by 4% on 2012, rising to more than 14.5 million, with sales rising 11% to just over £585.5m, according to figures from the Society of London Theatre.