Radiohead lead guitarist and keyboardist, Greenwood, was nominated for his score of the 2017 film Phantom Thread directed by Paul Thomas Anderson.
The historical drama also received a nomination for Best Original Score at last year's Golden Globe Awards.
Since turning his hand to film scoring in 2003, Greenwood has composed for films including We Need to Talk About Kevin, The Master and You Were Never Really Here.
Oscar-winning film composer Marianelli was nominated for his score of The Darkest Hour, a 2017 British war drama film starring Gary Oldman as Winston Churchill.
The film was his fifth time collaborating with director Joe Wright, following scores for Pride & Prejudice, Atonement, which won him an Oscar and a Golden Globe, The Soloist and Anna Karenina.
The nominations were announced today and the ceremony is set to take place on 18 February at London's Royal Albert Hall.