Sissons, whose broadcasting career spanned more than 40 years, died on Tuesday while surrounded by family, his agent said in a statement.
"We are sad to announce that Peter Sissons, the former presenter on ITN, Channel 4 and the BBC, died peacefully last night in Maidstone Hospital, Kent.
"His wife and three children were with him and wish to pass on their thanks to the hospital staff who were so caring and fought gallantly to save him to the end."
Veteran newsreader Sissons was a familiar face for decades as a newsreader, joining ITN in 1964 after graduating from Oxford University.
In 1969 he was appointed ITN's news editor, becoming industrial correspondent a year later, and industrial editor in 1972.
His first role as a news anchor came several years later when he began presenting ITN's News At One.
Sissons joined the BBC in 1989 as presenter of Question Time, as well as joint presenter of the Six O'Clock News.
He moved to the Nine O'Clock News in 1994 and stayed with the programme until it moved to its new time of 10pm.
He retired from broadcasting in 2009 and was considered at the time to be one of the UK's longest-serving news presenters.
BBC journalist Simon McCoy was among those paying tribute, writing on Twitter: "Very sorry to hear of the death of former colleague Peter Sissons. A great journalist and a fine presenter at ITN and the BBC. #RIP"