His professional baseball career began in 1947 with the Henderson Oilers, an unaffiliated team in the Class C Lone Star League.

Tappe made his major league debut on April 24, 1954, as a late-inning defensive replacement for Chicago catcher Joe Garagiola, and would appear in 145 games for the Cubs over all or parts of six seasons during the next nine years.

However, he would prove valuable to the Cubs as the author of their organization-wide instruction manual, and as a "motivator with an enthusiastic attitude" whose "strength was in the development of pitchers and catchers".

During the 1960–61 off-season, according to his account, he suggested to owner Wrigley that he not allow Lou Boudreau's successor as manager to bring in his own coaches, as had long been standard practice.

Since he notched a 42–54 record in 1961—by far the best of the four who led the club—it was generally believed that he would remain head coach as long as the Cubs were playing well.