He had a career in stage, television and film which spanned more than 70 years.
Paying tribute, Hardy's children said: "Dad is remembered as a meticulous linguist, a fine artist, a lover of music and a champion of literature, as well as a highly respected historian, and a leading specialist on the longbow.
"He was an essential part of the team that raised the great Tudor warship The Mary Rose. He is celebrated by all who knew him and loved him, and everyone who enjoyed his work."
The statement added: "We are immensely grateful to the team at Denville Hall [a home for retired actors] for the tender care they gave during his last weeks."
Robert Hardy's All Creatures Great and Small co-star Christopher Timothy paid tribute to the actor.
He said: "I was very sad to hear about Robert today, he played a big part in something that was an important phase of my life. We did meet up last year at a Herriot function and although he looked frail he still had his wit and humour. Great to see him.
"He has left an unbelievable legacy of fantastic work for many generations to enjoy and appreciate. A fascinating man, he didn't suffer fools I can tell you, but he was a good fellow. Prince Albert and of course Campbell were just two of the performances that stick in my mind. May he rest in peace."
A familiar household face, Hardy was also known for his roles in TV shows Middlemarch and Little Dorrit, and took on the role of former British prime minister Winston Churchill in Churchill: 100 Days That Saved Britain (2015) and in Winston Churchill: The Wilderness Years (1981).
The Bafta-nominated star, from Cheltenham in Gloucestershire, was also awarded a CBE for his services to acting in 1981.
One of his earliest TV jobs, in 1955, saw him take on Shakespeare as he portrayed Cassio in Othello.
Within minutes of the announcement of his death, a Tweet from London's Westminster Abbey read: "Robert Hardy read from Henry the Fifth at our 600th Anniversary of the Battle of Agincourt service in 2015. RIP."
The British Film Institute (BFI) posted: "We're sad to hear Robert Hardy, best known for roles in the Harry Potter films & TV series All Creatures Great And Small, has died aged 91."
His former Oxford school, Magdelen College, added: "Sad news breaking that Magdalen alumnus Robert Hardy (1944) has died at the age of 91."
