Born in 1947 in Rhodesia, now Zimbabwe, Anderson was educated at Prince Edward School. His father commanded the Rhodesian Army and his mother Daphne, wrote a memoir of her difficult childhood in Rhodesia. He has appeared in the US television series, Criminal Minds, as well as the ongoing show Ultimate Force in which he played Colonel Aiden Dempsey for the entirety of its production. He had previously played Lt. Col. Dan Fortune in ITV's Soldier Soldier (series 1 and 2 only, 1991–92). He was awarded the 1982 London Critics' Circle Drama Theatre Award for Best Supporting Actor of 1981 for his performances in The Twin Rivals and The Witch of Edmonton. His numerous performances for television include Fall of Eagles, Z-Cars, The Sweeney. Campion, House of Cards, Oliver's Travels, Every Woman Knows a Secret and Holby City. Anderson has also appeared in two episodes of Midsomer Murders entitled "Death In Disguise" and "Last Year's Model", and was the voice of Poseidon in the 1997 TV adaptation of The Odyssey. Most recently he was seen as Major Marchbanks in the BBC adaptation of Philip Pullman's The Ruby in the Smoke and he appeared in 2007 in the sixth series of the crime-drama Waking the Dead. In 2008, he made a brief appearance as Edward Tunstall in the BBC's EastEnders. He narrated the Sky1 version of the New Zealand documentary The Lion Man and appeared in an episode of A Touch of Frost. In 2010, Anderson appeared as the title character in The Madness of George III mounted by Director Adrian Noble at San Diego's Old Globe Theatre. He won the San Diego's Critics' Circle award for Best Actor. In 2011, he played Prospero in The Tempest and Salieri in Amadeus, both directed by Noble. In 2013 he again won the San Diego Critic's Circle Award for his Shylock in Adrian Noble's production of Shakespeare's The Merchant of Venice. In 2015 he appeared as Renard in the BBC TV series The Musketeers episode 2.5 "The Return". His film credits include roles in The Thirty Nine Steps (1978), The Shillingbury Blowers (1980), Sky Bandits (1986) and Cry Freedom (1987), among others.

He is an associate member of RADA and the father of actor Joe Anderson and Max Anderson the 2006 and 2011 World Streetboard Champion.