Alberts was born in Cedar Falls, Iowa to parents Ken Alberts, a business executive, and Linda. He also has an older brother, Troy, who went on to work as a sales director in an oil processor, and a sister, Tami, who teaches elementary school. Trev Alberts attended Northern University High School in Cedar Falls, where he played for the Northern University Panthers high school football team.
While attending the University of Nebraska, he played for the Nebraska Cornhuskers football team from 1990 to 1993. Following his senior season in 1993, he was awarded the Dick Butkus Award and Jack Lambert Trophy as the top college linebacker; Alberts was also recognized as a consensus first-team All-American, after recording 15 quarterback sacks, 21 tackles for loss, and 38 quarterback hurries. Despite an injury early in the eleventh game of the season against the Oklahoma Sooners, Alberts returned with a cast on his arm for the national championship game against Florida State in the Orange Bowl. Although the Seminoles won 18-16, Alberts had a dominant performance with three sacks of Heisman Trophy-winner Charlie Ward (FSU quarterbacks were sacked only five times during the 1993 regular season).
Alberts was hired in April 2009 to be the director of athletics for the Nebraska–Omaha Mavericks sports program at the University of Nebraska-Omaha.
I believe the potential for UNO's athletic programs is unlimited. This new chapter in my life will be exciting for me and for my family. I had an amazing experience as a college athlete. For several years now, I’ve wanted to return to college athletics and give something back. This position at UNO is a privilege.
—Alberts upon assuming the UNO job