Born in Fort Lauderdale, Florida, Morse lived with his siblings and grandparents in Jamaica until the age of six when he moved back to his birthplace. Morse, raised by his single mother, attended Nova High School in Davie, Florida, the alma mater of fellow major leaguer Anthony Swarzak. At Nova High, Morse was also a quarterback for the football team, following in the footsteps of his older brother, T.K.

Morse was selected by the Chicago White Sox in the third round (82nd overall) of the 2000 Major League Baseball Draft as a shortstop. During his time in the minors, Morse primarily played shortstop and also filled in as a third baseman.

Morse was acquired by the Mariners along with Miguel Olivo and Jeremy Reed for Freddy Garcia and Ben Davis on June 27, 2004. Beginning the 2005 season with the Triple-A Tacoma Rainiers, he made his major league debut on May 31, 2005. Although Morse made it to the big leagues as a shortstop, with the arrival of Yuniesky Betancourt, Morse began to develop as a utility player, having spent time at first base and left field. In 2005, he was suspended for 10 days for using performance-enhancing drugs.

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