When he took an interest in acting at age 18, he joined the National Youth Theatre and then studied at the London Academy of Music and Dramatic Art (LAMDA). (He now serves as a council member for LAMDA.)
In 1973, he joined the Royal Shakespeare Company. The 1970s also saw his first appearance on screen. His first appearance on film came with 1980's A Tale of Two Cities. He was awarded the Royal Television Society's award for best male actor for A Song for Europe in 1985. His performance as the title character in Poirot earned him a 1991 BAFTA TV Award nomination. He was given a Variety Club Award in 1994 for best actor for portraying John in David Mamet's play Oleanna at the Royal Court Theatre. Suchet later won another Variety Club Award for his portrayal of Antonio Salieri in Amadeus.
Suchet was nominated for another Royal Television Society award in 2002 for his performance as Augustus Melmotte in The Way We Live Now, which also earned him a BAFTA nomination. The same year he was appointed an OBE by Queen Elizabeth II.
He has also appeared in a number of films, including Executive Decision (1996), A Perfect Murder (1998), and Wing Commander (1999).
David is the brother of John Suchet, an ITV News presenter. David married Sheila Ferris in 1976.