A 5’11”(1.80 m ) tall[1][2] point guard, he reached star status in the EuroLeague, mainly while playing with Olympiacos, under head coach Dušan Ivković.

He contributed to the team winning three State Championships and became the school's first player to be invited to the McDonald's All-American Game (1984).

[3] Rivers accepted a basketball scholarship from the University of Notre Dame, to play under head coach Digger Phelps.

On August 24, 1986, before the start of the season, he was a passenger in a van being driven by former college teammate Ken Barlow, returning to an apartment they shared after working a summer job with a caterer business, when the vehicle overturned and went into a ditch, after trying to avoid an oncoming car.

On July 12, 1991, he was traded to the La Crosse Catbirds of the Continental Basketball Association, playing under coach Flip Saunders.

In the 1997 off-season, Rivers left Olympiacos to join Italian League club Teamsystem Bologna, playing alongside former NBA All-star Dominique Wilkins.

He averaged 12.8 points, 3.3 assists per game and contributed to the team winning the Italian Basketball Cup, receiving Co-MVP honors with teammate Carlton Myers.

[18] In 2000, he returned to play with Olympiacos B.C., contributing to the team reaching the Greek Basket League Championship game, where it lost to Panathinaikos B.C.

Although he didn't play for 2 years, he then signed with Olympique Antibes for the 2003–04 season in the second division of the LNB Pro A French League.

In 2009, he was hired as a coach by Virtus Bologna of the Lega Basket Serie A, to assist in the development of junior players that season.