Verlander, who kept the Cleveland Indians out of the hit column into the sixth inning in Game 1 of the American League Division Series, will start opposite Chris Sale in the series opener on Saturday.
During the regular season, Verlander made one start against the Red Sox - coming at home - and lasted six innings. He allowed two earned runs on three hits and struck out six during the outing.
Cole, who struck out 12 in Game 2 of the ALDS, will square off against Red Sox left-hander David Price the following night at Fenway Park.
In two regular-season starts against the Red Sox, Cole allowed five earned runs and 10 hits in 13 innings, while striking out 15.