A third team All-American in 1986-87 and a second team selection in '87-88, he attended the University of Notre Dame.
He was the co-captain of the '87-88 squad. He currently ranks fourth in school history, in scoring with 2,058 points, and second in Notre Dame history in assists (586). He also ranks second all-time in steals (201) and steals average (1.7 spg), second in games started (116), fourth in assists average (5.0 apg) and three-point field goal percentage (.406), ninth in games played (118), 11th all-time in three-point field goals made (67) and 13th in three-point field goals attempted (165). He was selected to the 1987 NCAA Championship All-Regional team. He earned four monograms while a member of the Fighting Irish.
Rivers was selected 25th overall by the Los Angeles Lakers in the first round of the 1988 NBA Draft, receiving very little playing time in his rookie season. Rivers was drafted by the Minnesota Timberwolves in the 1989 Expansion Draft, but was waived before playing a game. He had two more seasons of no impact with the other Los Angeles team, the Clippers (1989–90 and 1991–92).
He averaged 17 pts, 3.4 assists, 2 steals and 37.9 minutes in 23 games. In 1997 Rivers left Olympiacos to join Teamsystem Bologna and played alongside former NBA all-star Dominique Wilkins. He later played for Tofaş Bursa in Turkey where they won two league championships and two cups before re-joining Olympiacos for one season.