The 75-year-old details his experiences with the illness in a new biography of his life coming out in his native the Netherlands.
Jansen, who played in two World Cup finals for the Dutch national side, is a hero in the east end of Glasgow for leading the Hoops to the Scottish Premier Division title in 1998, stopping rivals Rangers at nine titles in a row and denying them a record-setting tenth.
Celtic tweeted out a club statement on Monday afternoon, which read: "Everyone at Celtic would like to send their best wishes to our former manager, Wim Jansen, after he revealed this week that he is living with dementia.
“Wim will be forever held in the highest regard by the Celtic Family for his success in winning the league title for the club back in the 1997/98 season, the year when the Hoops famously ‘stopped the 10’.
“Wim’s Celtic connection goes back even further, however, as he was part of the Feyenoord side which beat Celtic in the 1970 European Cup final.
“As Celtic manager, he brought Henrik Larsson to Paradise from Feyenoord, and in his season in charge of the Hoops, Wim also won the League Cup as well as the league title.
“Our thoughts are with Wim and his family, and the best wishes of the whole Celtic Family are with a man who delivered one of the most important title triumphs in the club’s history.
“Wim, You’ll Never Walk Alone.”