Benson died on Thursday after a short illness.
He was known for playing the Yorkshire-based drama's funeral director in all of the show's 18 series during its run from 1992 to 2010.
His character also ran a garage in the fictional town of Aidensfield and often got involved in disastrous money-making schemes with Claude Greengrass (Bill Maynard) and half-brother Vernon Scripps (Geoffrey Hughes).
Benson also made appearances in BBC comedy Blackadder as Henry VII, ITV 1980s soap opera Albion Market and more recently in two episodes of hospital drama Casualty.
Benson was a highly-skilled singer and dancer and an accomplished theatre actor. He and Maynard starred on stage together in a production of Trinity Tales in 1977.
He portrayed the title role in Shakespeare's Henry VI in a BBC television adaption of the play in 1983.
One of Benson's former Heartbeat co-stars Steven Blakeley, who played Pc Geoff Younger in the show, was among those to pay tribute to him.
Blakeley said: "Farewell Peter Benson. You made me laugh so much. There'll never be another like you - talented, kind and gentle in equal measure. Bless you and rest well sir."
Lisa Kay, who played the character of Emma Bryden, wrote on social media: "Such sad news that the wonderful Peter Benson has passed away.
"He was always a total gentleman and great fun to work with. He was dearly loved and shall be missed terribly by his Heartbeat family. RIP Peter."
Fiona Dolman, who played Pc Mike Bradley's (Jason Durr) solicitor wife Jackie, added: "What sad news. Peter Benson was one of the best.
"Kind, funny, brilliant, gentle and deliciously sarcastic. He was an absolute joy to work with and will be missed by so many."