The Russian billionaire will reportedly spend £5 million on the party for his 300 specially invited guests, according to the Daily Telegraph.
The band will play a set at the exclusive party, to be held at his £58 million estate on the Caribbean island of St Barts.
Invited guests will wear "island chic" clothing for the event, running from 10pm to 4am, after which they will be able to stay on a fleet of super-yachts in the marina.
In 2009, the likes of Orlando Bloom and Kanye West attended the Chelsea football club owner's end-of-year party, with Prince, Gwen Stefani and Beyoncé performing for guests.
Abramovich owns a £300m super-yacht at the island, which includes a cinema, library, restaurant and accommodation for 12 guests.
Red Hot Chili Peppers will play three huge stage shows across the UK and Ireland next summer.
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