He played in Major League Baseball (MLB) from 1988 to 1999 for the Texas Rangers, Milwaukee Brewers, Boston Red Sox, St. Louis Cardinals, Seattle Mariners, Chicago Cubs, and New York Yankees.

Fossas attended St. Mary's High School in Brookline, Massachusetts, and was selected as a 12th round pick by the Texas Rangers during the 1979 Major League Baseball draft.

The previous year he had been drafted by the Minnesota Twins, but decided not to sign with the team, instead finishing his college studies and collegiate career at University of South Florida in Tampa.

Although he only pitched 5+2⁄3 innings that initial year, Fossas eventually became an entrenched yeoman setup pitcher with the Milwaukee Brewers from 1989 to 1990, the Boston Red Sox from 1991 to 1994, and the St. Louis Cardinals from 1995 to 1997.

In 1998 he pitched for the Seattle Mariners, Chicago Cubs and returned to the Texas Rangers in what would be his last full year before finishing his career with the New York Yankees in 1999.