Anderson's stop-motion kid-flick is adapted from Roald Dahl's book about the battle between a suave, chicken-stealing fox and evil farmers Boggis, Bunce and Bean.
Jason Schwartzman, Bill Murray, Willem Dafoe, Michael Gambon and musician Jarvis Cocker also provide voices for the playfully lo-fi feature, which brings the hipster sensibility of Anderson's "Rushmore" and "Royal Tenenbaums" to Dahl's children's classic.
Although the film takes liberties with Dahl's story - giving Mr. Fox additional neighbors and family members - the filmmakers had the blessing of Dahl's widow Felicity. Anderson and co-writer Noah Baumbach even wrote the screenplay while staying at the Dahl family home in Great Missenden, southern England.
"Fantastic Mr. Fox" is released in Britain Oct. 23 and in the United States next month.
Clooney is a major presence at this year's festival, also playing a psychic researcher for the U.S. military in Grant Hestov's "The Men Who Stare at Goats" and a smooth management consultant in Jason Reitman's "Up in the Air."
One of the world's oldest film festivals, London is trying to raise its international profile to compete with better-known events in Cannes, Venice and Toronto. Most of the 300 films from almost 50 countries in the London lineup have been screened elsewhere, but 15 are world premieres.
The festival also plans to hand out a best-picture prize for the first time at an awards ceremony on Oct. 28.
The lineup includes Austrian director Michael Haneke's "The White Ribbon," which won the top prize at this year's Cannes Film Festival; prison drama "A Prophet" from France's Jacques Audiard; Jane Campion's visually ravishing John Keats biopic "Bright Star"; "Steven Soderbergh's whistle-blower saga "The Informant"; designer Tom Ford's directorial debut "A Single Man"; and Lone Scherfig's "An Education," the Nick Hornby-scripted story about a teenager coming of age in the 1960s.
The festival wraps up Oct. 29 with the world premiere of "Nowhere Boy," a film about the young John Lennon directed by British artist Sam Taylor-Wood.