A navy brat, he spent most of his childhood moving to different cities. According to his autobiography, he began playing baseball at the age of 3. After the Vietnam War his father became a recruiter for the United States Navy and his family settled in Texas. Due to the fact his school did not have a baseball program, he played football but never gave up on his dreams of becoming a professional baseball player.

In January 1983, Morris was selected in 4th overall in the January portion of baseball's amateur draft. He suffered several arm injuries in the minor leagues, and was released during the 1987 season. He caught on with the White Sox organization for 1989, but was unable to make something of his career, and retired to become a high school physics teacher and baseball coach in Big Lake, Texas.

The team (Reagan County High School) often lost a lot of games but in 1999, Morris inspired the club to play better. They made a bet that if they won the title, Morris would attend a major league tryout. Sure enough, they were district champions, and Morris followed up on the deal by trying out for the major leagues.

The major league scout for the Tampa Bay Devil Rays initially wasn't interested in Morris, but agreed to allow him to tryout so Morris could keep his promise with his students. Surprisingly, Morris discovered that in spite of his age, and having several surgeries on his arm, he was able to throw a 98 mph fastball. He immediately earned a spot on their AAA club, the Durham Bulls. Thanks to solid performances with Durham, Tampa Bay gave him a chance to pitch with the big club when the rosters expanded, and on September 18, 1999, against Royce Clayton of the Texas Rangers, the 35-year old Morris made his debut, striking out Clayton on 4 pitches. His goal of pitching in the majors was finally realized, and he made 4 more appearances later that year.

His arm problems recurred limiting him in 2000 to only 21 major league appearances, after which the Rays released him. He attempted to catch on with the Dodgers the following spring but wasn't able to overcome his injuries. At the end of his major league career he was 0-0 with an ERA of 4.80 and 13 strikeouts.

His story is well documented in his autobiography, The Oldest Rookie (ISBN 0-31-659156-4), and in 2002, it was translated to the silver screen by Disney as The Rookie, starring Dennis Quaid. Since his retirement, he's become an in-demand motivational speaker and devotes much of his spare time to coaching high school baseball teams in the Dallas area.