The Oscar-nominated actor, who was also a committed Christian, died from heart failure at his home in Surrey on Saturday following a short illness.
Frank Finlay's career spanned more than 60 years and he appeared in productions for both stage and screen, including the 1965 film Othello and The Three Musketeers in 1973.
Paying tribute, his family said: "Goodbye to a wonderful father, loving grandfather and a damn fine actor. At home, very peacefully, surrounded by his family."
Two of his children, Daniel and Cathy, added: "Our dad was a magnificent actor - honest, uncompromisingly truthful, rigorous, fearless and funny.
"As a loving father and besotted grandpa, he held his family at the centre of his life. He and our mum, Doreen, had a long and happy marriage and together they loved and looked after us all. We are all immensely proud of him."
Actors to honour Frank Finlay include Mark Gatiss, who said: "Bouquets to the great Frank Finlay. Musketeer, vampire hunter, green-eyed Iago.
"A wonderfully fiery presence on stage and screen. RIP."
Sir Roger Moore described Finlay as "a great co-star" in 1978's The Wild Geese.
John Challis, who played Boycie in Only Fools And Horses, said: "Such sad news to hear that dear Frank Finlay has died. Happy times with him touring Laughter on the 23rd Floor."
Born in 1926 in Lancashire, Finlay landed his first professional role in Scotland in 1951, before winning a scholarship to London's Royal Academy of Dramatic Art.
He made his first appearance in the West End when he was 31 and, following a series of acclaimed performances, he was invited to join Laurence Olivier's National Theatre Company.