Johnson made his film debut in the 1950s and featured in numerous films, alongside stars such as Frank Sinatra, Laurence Olivier and Charlton Heston.
A founder member of the Royal Shakespeare Company, Johnson played several lead roles including Romeo and Mark Anthony in Julius Caesar.
He also appeared in several TV dramas such as Lewis and Silent Witness.
Johnson died after a short illness at the Royal Marsden Hospital in Chelsea, London. He is survived by his wife Lynne, who he married in 2004, and his four children.
Johnson was born in Upminster, Essex, and he left his training at the Royal Academy of Dramatic Art (RADA) to join Sir John Gielgud's company.
He joined the Royal Navy during World War Two and then made his film debut in 1959, when he appeared in the MGM film Never So Few, starring Frank Sinatra and Gina Lollobrigida.
He also appeared in The Haunting (1963) and Khartoum (1966), opposite Laurence Olivier and Charlton Heston.
His family said he was offered and turned down the role of James Bond after playing British spy Bulldog Drummond in Deadlier Than the Male (1967) and its sequel Some Girls Do (1969).
His most recent film credits include The Boy in the Striped Pyjamas (2008) and Lara Croft: Tomb Raider (2001).

The Premier League club say the 22-year-old left-back is expected to be sidelined for "up to eight weeks" after the knock in a 6-1 loss to Bournemouth.
"The Scottish international damaged his calf during the second half of the defeat," said a club statement.
Scotland will face England in World Cup qualifying Group F on 11 November.
Gordon Strachan's side sit three points behind leaders England after three games.
The Scotland head coach had remarked before this month's 1-1 draw with Lithuania that his squad had "incredible" strength in depth at left-back.
Robertson started at Hampden but picked up a knock and Celtic's Kieran Tierney took over for the 3-0 defeat in Slovakia.
Hull were 3-1 down at the Vitality Stadium when they lost Robertson to injury after 63 minutes, defeat knocking them down to 16th, two places and one point above the relegation spots. The game was Mike Phelan's first since his appointment as head coach until the end of the season following a spell as caretaker.
The left-back said on Twitter: "Looks like I'll be a supporter for the next few weeks! Hopefully the lads can kick on."
Robertson's Scotland team-mate, goalkeeper David Marshall, has endured a miserable spell since his transfer from Cardiff City, conceding 15 goals in his first four outings for the Tigers.
British actor Richard Johnson, whose career spanned film, theatre and TV, has died aged 87, his family has said.
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Andrew Robertson will miss Scotland's trip to Wembley to face England and up to 10 games for Hull City after suffering a calf injury.