Bill appeared on the soap for more than 30 years playing the character of Jack Duckworth, husband of Vera Duckworth.
Nigel Pivaro, who played the couple's layabout son Terry, described Tarmey as a "second father" and a "wise and dignified man who taught me a great deal".
Julie Goodyear, who is better known as the Rovers Return bar maid Bet Lynch, described Bill as a "wonderful man" and said he would be "sadly missed."
Fellow Corrie actor Michael Le Vell, who played the mechanic Kevin Webster, said he became close friends with Bill soon after his father died.
"He and Liz [Dawn who played Vera Duckworth] looked after me and got me through those early days and we've been friends ever since. I am going to miss him very much."
Alan Halsall, whose character Tyrone dobbs looks to Jack a father figure, described Bill as "super talented".
"He guided me when I joined as a young actor and would do anything for anybody," he added.
According to TV presenter Eamonn Holmes, Bill "always remembered the small things".
Tributes have also flooded in from members of the public on ITV News' Facebook page.
Stephanie Thrall from Manchester described him as a "genuinely lovely man" while Helen Keane-Wison said the "brilliant actor" would be "sadly missed by everyone".
Dawn Kinsley friom Kingston upon Hull said he was a "brilliant and much-loved actor and a lovely person".
"He will be missed in the TV world as we missed him on coronation street."