He was born Nicholas Conte in Jersey City, New Jersey, the son of a barber.

In 1935, Conte was spotted by Elia Kazan and John Garfield when he was working as an entertainer at a Connecticut resort, which led to Conte finding stage work. Conte eventually earned a scholarship to study at the Neighborhood Playhouse in New York, where he became a standout actor. The 5' 8" Conte became a Broadway actor in the late 1930s, starring in such plays as Night Music and Walk Into My Parlor. That lead to his first film performance in 1939, Heaven with a Barbed Wire Fence.

In 1942 he signed a long-term contract with 20th Century Fox. He then changed his stage name to Richard. His first film at Fox was Guadalcanal Diary (1943). During the World War II years, Conte played mostly soldiers in war dramas, including A Walk in the Sun (1945).

Following the war, Conte appeared in many films noir after World War II. Conte appeared in such Fox crime dramas as Cry of the City and Call Northside 777 (both from 1948).

In the early 1950s, Conte, now not working for Fox, began appearing in films for various studios. Critics and fans consider his best films from that era include the film noir B-movies Highway Dragnet (1954) and The Blue Gardenia (1953).

Once film noir became less popular in the 1960s Conte’s career was at a standstill. He appeard as Lt. Dave Santini in two Frank Sinatra crime films, Tony Rome (1967) and Lady in Cement (1968). He eventually moved to Europe and acted in a number of films. Later in life, Conte acted one of his most memorable performances in The Godfather (1972) as Don Barzini (he was at one time also considered for title role, a role that Marlon Brando eventually filled.) He continued to work in European films until a heart attack in 1975 at the age of 65.

He is the father of film actor Mark Conte.