Rivera was signed by the Yankees as a non-draft amateur free agent in 1996 and made his debut in the 2001 season. When he came up to New York in midseason 2002, and while he showed promise, his .265 of batting average and one home run was a disappointment for the Yankees standard.
Rivera was sent to Triple-A Columbus in 2002. Rivera was again recalled in 2003, this time to hit seven homers (including a multi-homer game) with 26 RBI. Although he is not known for his speed, Rivera is considered an above average fielder who gets a good jump on the ball, has a strong throwing arm, and is adept at playing the outfield corners: left and right field. He was traded to the Expos before the 2004 season. In Montreal he finished with a .307 batting average, 12 homers and 49 RBIs in 2004.
On November 19, 2004, he was sent along with shortstop Maicer Izturis to Anaheim in the same trade that brought outfielder José Guillén to the Washington Nationals. In his first season as an Angel, Rivera saw playing time as both an outfielder and a designated hitter. Although he started the season slowly, he stepped up his play in the final months of 2005 and finished with a .271 batting average and a then-career high 15 home runs and 59 RBIs in 106 games.
During the 2006 campaign, Rivera was made an everyday player, often starting at left field (or serving as the designated hitter when veteran Garret Anderson plays left). As of September 2006, Rivera is having his best statistical year yet, batting .302 with 21 home runs and 74 RBIs.
- Signed as a non-drafted free agent by New York Yankees (April 12, 1996).
- Traded by New York Yankees with Nick Johnson and Randy Choate to Montreal Expos in exchange for Javier Vazquez (December 16, 2003).
- Traded by Washington Nationals with Maicer Izturis to Anaheim Angels in exchange for Jose Guillen (November 19, 2004).