Conine was born in Tacoma, Washington, played baseball at UCLA, and was drafted in the 58th round of the 1987 Major League Baseball draft by the Kansas City Royals. After two cup of coffee stints with the Royals, Conine was selected by the Marlins in the 1992 Major League Baseball expansion draft. Becoming the team's first star, he played five seasons with the Marlins, earning the most valuable player award at the 1995 Major League Baseball All-Star Game and earning a World Series title in 1997.