Amini wrote the adapted screenplay for The Wings of the Dove, which was based on the 1902 eponymous novel by Henry James. The film, directed by Iain Softley, was released in 1997 and received critical claim. Amini was nominated for an Academy Award for Best Writing – Adapted Screenplay.

Amini's first screenplay was for the 1994 TV movie The Dying of the Light, directed by Peter Kosminsky. The TV movie told the story of Sean Devereux, an aid worker who was murdered in Somalia in 1993 for criticising arms sales. It was nominated "Best Single Drama" at the British Academy Television Awards. Amini also wrote an adapted screenplay of the 1895 novel Jude the Obscure by Thomas Hardy. Producer Andrew Eaton commissioned the screenplay in 1995, and it was filmed by Michael Winterbottom as Jude, released in 1996. Amini also wrote a screenplay for another TV movie, Deep Secrets, which aired in 1996.

Amini was one of the screenwriters, along with Michael Schiffer, who wrote a screenplay adaptation of A.E.W. Mason's novel The Four Feathers, which became the film The Four Feathers (2002), directed by Shekhar Kapur and starring Wes Bentley and Heath Ledger. In 2008, he adapted the Elmore Leonard novel Killshot into the screenplay for the film Killshot (2008), directed by John Madden and starring Thomas Jane, Diane Lane, Mickey Rourke, Joseph Gordon-Levitt, and Rosario Dawson.

In 2010, Amini wrote an original screenplay for a film entitled Shanghai directed by Mikael Håfström and starring Chow Yun Fat, Gong Li, Ken Watanabe and John Cusack.

Amini also wrote the screenplay for the neo-noir film Drive (2011), directed by Nicolas Winding Refn. His screenplay for the film is a loose adaptation of the novel of the same name by James Sallis. During interviews, Refn noted that he and Amini cut out a lot of the content from Sallis' book, resulting in the almost bare bones structure for the film, and the few lines of dialogue for the film's star, Ryan Gosling. For his screenplay of Drive, Amini also won a "Best Adapted Screenplay" award from the Austin Film Critics Association in 2011.

Amini was one of the screenwriters, along with Evan Daughtery and John Lee Hancock, who wrote the screenplay for Snow White and the Huntsman (2012), directed by Rupert Sanders and starring Kristen Stewart, Chris Hemsworth and Charlize Theron. Additionally, Amini is one of the screenwriters, along with Chris Morgan and Walter Hamada, who wrote the screenplay for the film 47 Ronin (2013), directed by Carl Rinsch and starring Keanu Reeves, Hiroyuki Sanada, Tadanobu Asano, Cary-Hiroyuki Tagawa and Rinko Kikuchi.

In September 2013, Amini delivered a screenwriting lecture as part of the BAFTA and BFI Screenwriters' Lecture Series. He has also given lectures at the Central Film School.

His feature directorial debut, The Two Faces of January (2014), is a film adaptation of a Patricia Highsmith novel for which he also wrote the screenplay adaptation. The film stars Viggo Mortensen, Kirsten Dunst and Oscar Isaac. Mick LaSalle describes The Two Faces of January as having "the allure of a thriller and the haunting quality of a character study."

Amini adapted John le Carré's novel Our Kind of Traitor into a feature film screenplay directed by Susanna White. The film, Our Kind of Traitor, was released in 2016. The film stars Ewan McGregor, Naomie Harris, and Stellan Skarsgård.