Morrison was selected 39th overall in the 1993 NHL Entry Draft by the Devils after a season in the British Columbia Junior Hockey League (BCJHL); he had won rookie of the year honours for the Interior Conference as a member of the Penticton Panthers. Following his draft, he joined the college ice hockey ranks with the Michigan Wolverines of the Central Collegiate Hockey Association (CCHA). During his four-year collegiate career, he was named the NCAA Tournament MVP while leading the Wolverines to a national championship in 1996 and won the Hobey Baker Award as the NCAA's player of the year in 1997.