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Both movies are nominated for best picture, along with The Big Short, Bridge of Spies, Brooklyn, The Martian, Room and Spotlight.
Eddie Redmayne competes against Leonardo DiCaprio for the best actor award.
Charlotte Rampling is in the running for best actress, while Kate Winslet is up for best supporting actress.
Eddie Redmayne, nominated this year for his role as transgender pioneer Lili Elbe in The Danish Girl, won the 2015 Academy Award for his performance as Stephen Hawking in The Theory of Everything.
Leonardo DiCaprio, the star of survival epic The Revenant, has been nominated four times but has yet to win an Academy Award.
The best actor category also sees nominations for Michael Fassbender for biopic Steve Jobs, Matt Damon for space saga The Martian and Bryan Cranston for Trumbo, in which he portrays real-life Hollywood screenwriter Dalton Trumbo.
Charlotte Rampling, who receives a nod for marital drama 45 Years, faces competition in the best actress category from Cate Blanchett for Carol, Brie Larson for Room, Jennifer Lawrence for Joy and Saoirse Ronan for Brooklyn.
Other hopefuls include best supporting actor nominees Christian Bale, for The Big Short, Mark Rylance, for Cold War thriller Bridge of Spies, and Tom Hardy for The Revenant.
Nick Hornby is nominated for best adapted screenplay for Colm Toibin’s Brooklyn, with fellow British author Alex Garland honored for his original screenplay for Ex Machina.
Singer Sam Smith is nominated for best original song for Writing’s On the Wall, having already won a Golden Globe for the SPECTRE track alongside writing partner Jimmy Napes. They will compete with singles including Lady Gaga’s track Til It Happens To You, from The Hunting Ground, and The Weeknd’s Earned It, from Fifty Shades Of Grey.
In the best documentary feature category, Amy Winehouse documentary Amy secures a nomination for London-born filmmaker Asif Kapadia and James Gay-Rees.
Movies which also scooped a handful of nominations were The Martian with seven nods, while real-life journalism drama Spotlight, Steven Spielberg’s Bridge of Spies and Cate Blanchett romance Carol have six each.
The Big Short, about the 2008 financial crisis, and Star Wars: The Force Awakens are in the running for five awards.
Room, based on the novel by Irish writer Emma Donoghue about a mother and son living in confinement, picked up four nominations, including best adapted screenplay.
The film’s director Lenny Abrahamson was also nominated.
Sylvester Stallone is nominated for the best supporting actor award for his comeback performance as Rocky Balboa in Creed, having won a Golden Globe for the movie last weekend.
Mark Ruffalo completes the category, having been cited for his role in Spotlight.
Pixar’s Inside Out is in the running for best animated feature film, with competitors including Charlie Kaufman’s Anomalisa and the Shaun the Sheep Movie, featuring the character first seen alongside Wallace and Gromit in Aardman’s A Close Shave.
Steven Spielberg has set the record for the most best picture nominations for an individual producer with nine, having been nominated for Cold War thriller Bridge of Spies.
The 88th Academy Awards, hosted by Chris Rock will be held at Hollywood’s Dolby Theatre on February 28.
Movies with most nominations:
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