Cheek, who died in 2005, called the first 4,306 regular-season and 41 post-season games of the Blue Jays franchise. He broadcast the franchise's first game April 7, 1977 and every game until June 2004, when he missed two games after the death of his father.
He took additional time off in 2004 following surgery for removal of a brain tumor but continued to call Blue Jays' home games during his chemotherapy regime.
"Tom Cheek was the voice of summer for generations of baseball fans in Canada and beyond," said Hall of Fame President Jeff Idelson.
"He helped a nation understand the elements of the game and swoon for the summer excitement that the expansion franchise brought a hockey-crazed nation starting in the late 1970s. He then authored the vocal narrative of a team that evolved into one of the most consistent clubs of the 1980s and 1990s.
"We are thrilled to celebrate Tom's legacy with baseball broadcasting's highest honor."
The Ford C. Frink Award honors baseball broadcasting excellence. A nominee has been inducted into the Baseball Hall of Fame each year since 1978 when Mel Allen and Red Barber were the honorees.
In 2011, Dave Van Horne won the Frick award for his long career broadcasting Montreal Expos games. In 1974, Cheek was a back-up announcer for Van Horne.
Cheek is to be honored at the Hall of Fame induction ceremonies July 27.