Wilson is the son of Georges Wilson, who was an actor, theatrical manager and Director of the Théâtre National Populaire. As a teenager, he had little interest for the French theatre and aimed to become an "American actor" and appear in Hollywood pictures. He studied acting at the Drama Centre London in order to learn English. He played his first movie role in the 1977 American film Julia, directed by Fred Zinneman. Five years later, he played his first starring role in another film by Zinneman, Five Days One Summer, opposite Sean Connery. But the film was not a commercial success, and neither was Sahara in which Wilson co-starred with Brooke Shields. Wilson ultimately found success in his home country : during the 1980s, he became popular with French audiences by appearing in successful films such as La Boum 2, The Public Woman and Rendez-vous. At the time, he was often cast either as tormented characters or in romantic parts, although he found himself more convincing in the former kind of roles.

Wilson screen tested for The Living Daylights (1987) for the role of James Bond, appearing in test footage opposite Maryam d'Abo (the Bond girl in The Living Daylights) as Tatiana Romanova, re-enacting scenes from From Russia with Love (1963). Wilson was featured in a series of Calvin Klein ads featuring Christy Turlington for Eternity in 1991, as well as a poster ad, years later in 1998.

In 1989, his performance as abbé Pierre in the film Hiver 54, l'abbé Pierre, for which he received the Jean Gabin prize, won him critical accolades. In the late 1980s and early 1990s, however, his screen career suffered from a series of box office failures, such as The Possessed and El Dorado. He later said that the French producers had come, at the time, to regard him as "box office poison". He eventually won back the favors of French audiences by appearing in the successful comedies Same Old Song (1997) and Jet Set (2000)..

Wilson was cast in the role of the Merovingian in The Matrix Reloaded (2002) and The Matrix Revolutions (2003), perhaps his best-known role in the American cinema. Being completely fluent in English, his strong French accent in the film is fabricated for the role. The role also popularised the Ediety tie knot, now commonly referred to as "the Merovingian".

In November 2012, he was selected as a member of the main competition jury at the 2012 International Film Festival of Marrakech.

In April 2013, Wilson was invited by MINUSTAH (the United Nations Stabilization Mission in Haiti) to visit Haiti in the capacity of helping with various UN-backed environment and cultural programmes.

He was the master of ceremonies for the opening and closing ceremonies of the 2014 Cannes Film Festival and 2015 Cannes Film Festival.

In February 2016, he released a tribute album called Wilson chante Montand to the singer Yves Montand to commemorate the 25th anniversary of the death of the Artist. Among the 17 tracks on the album there is Mais qu’est-ce que j’ai ? which was composed by Henri Betti with the lyrics by Édith Piaf in 1947. The musical arrangements of the 17 songs were made by Bruno Fontaine. Also in 2016, he portrayed Jacques Cousteau in the biopic The Odyssey.

In January 2018 he engaged to assist the Food and Agriculture Organization of the United Nations (FAO) in communications regarding work to eradicate world hunger and poverty - 'Working for Zero Hunger.'

Wilson is Chevalier and Officier des Arts et des Lettres and Chevalier and Officier de l'Ordre National du Mérite. He was raised to Commandeur de l’Ordre du Mérite by President Emmanuel Macron in 2017.