A statement from the family of the Northern Ireland broadcaster said he passed away at his home in Surrey on Thursday, following a long illness.
They said: "While many people will remember John for his journalism and broadcasting, for us he was the most loving, funny and devoted husband, father and grandfather.
"We will miss him terribly, but have so many memories of the tremendous happiness he has brought into our lives."
John Cole was born in Belfast in 1927.
He spent 10 years with the BBC, where he served as Political Editor, after a lengthy career with newspapers including the Belfast Telegraph and The Guardian.
Mr Cole was the face of the channel's political coverage during the 1980s and covered major stories such as the Brighton bomb and the Falklands War.
He retired following the 1992 general election and is survived by his wife Madge, sons Donald, Patrick, David and Michael, and nine grandchildren.