The 79-year-old had been suffering from various illnesses, including pneumonia, and died in hospital, his agent said.
Janet Glass released a statement praising his “brave spirit and wonderful humour”.
It said: “Universally loved and admired through his unforgettable roles in classic productions such as Breaker Morant, The Wicker Man, Callan, The Equalizer and many more, he was equally fine and courageous in real life, never losing his brave spirit and wonderful humour throughout his illness.
“He was further sustained by the love of his wife, Michele, children, Tim, Peter, Sarah and Emily, his grandchildren and numerous friends. His passing will leave a huge gap in many lives.”
Woodward rose to fame in the 1960s and early 1970s in the television spy series Callan.
The cult film The Wicker Man, saw him play a devout Christian police officer drawn to investigating the disappearance of a young girl in a sinister community.
In the 1980s he gained international attention in the hit US TV series The Equalizer, playing a former spy turned gun-for-hire.
Woodward recently joined EastEnders for a short stint as Tommy Clifford, whose character drew out details of Patrick Trueman’s past.
Speaking about the role to What’s On TV earlier this year, Woodward said: “I was very pleased. I only like to do a few jobs each year and I pick the ones I can’t turn down. I liked the character and six episodes suited me.”
He said that as well as working on an autobiography, he had been spending time painting watercolours, adding modestly: “I am not very good at it, but my friends and family all get a copy.”
Woodward lived in the Padstow area of Cornwall, with his wife, actress Michele Dotrice, who is known for playing Frank Spencer’s long-suffering wife Betty in the classic sitcom Some Mothers Do ‘Ave ‘Em.
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