Rivera was drafted by the Seattle Mariners in the second round (49th overall) of the 2001 Major League Baseball Draft as a 17-year-old. He played most of the 2004 season with the High-A California League Inland Empire 66ers but played with both the Triple-A and Major League clubs in September. He made his Major League debut September 22, 2004, playing in two games for the Mariners that season as a late-inning replacement. Rivera began 2005 with the Double-A San Antonio Missions. He was promoted to the Mariners on May 15, but optioned back to San Antonio on May 20 without appearing in a game. He was again promoted to the Mariners on May 30 when starting catcher Miguel Olivo was sent down to Triple-A. On May 31, Rivera had his first Major League start and base hit, going 3 for 5 at the plate. Rivera shared catching duties with Pat Borders in June and was optioned back to San Antonio when Olivo returned. He played with the Triple-A Tacoma Rainiers in August and returned to the Mariners in September. In 2005, he had 12 starts at catcher and 19 hits in 48 at-bats at the Major League level.

Rivera was one of the final players cut from the roster in 2006 spring training and began the year at Triple-A. He was back with the Mariners by mid-April and served as a back-up to Kenji Johjima for the remainder of the season, batting .152 in 99 at-bats over 35 games. During the off-season, the Mariners weighed the benefits of allowing the young catcher to develop his hitting in the minor leagues against his providing limited offense in a back-up role in the Majors. In 2007, Rivera played for the Mariners Double-A affiliate, the West Tenn Diamond Jaxx, batting .214 in 91 games. He was granted free agency in November.

On November 22, 2007, Rivera signed a minor league contract that included an invitation to spring training with the Los Angeles Dodgers. The Dodgers assigned him to Double-A Jacksonville to begin the 2008 season. While at Jacksonville, Rivera began playing some first base, along with catcher, and was promoted to Triple-A Las Vegas on June 3. He hit .250 across both levels and was granted free agency at the end of the season.

Rivera signed with the New York Mets in November 2008. He spent the 2009 season with the Triple-A Buffalo Bisons, appearing in 63 games at catcher and 3 at third base. He hit .234 with 9 home runs.

On December 17, 2010, Rivera signed a minor league contract with the Minnesota Twins. His contract was purchased by the Twins on May 5, 2011. He was brought up from Triple-A to provide back-up to Drew Butera, who was the Twins' primary catcher with Joe Mauer on the disabled list. He went back to Triple-A in early July, but rejoined the team on August 28 when Mauer was sitting out. He finished the year with the Twins, hitting .144 in 104 at-bats over 45 games on the season.

Rivera was granted free agency at the end of the 2011 season, but re-signed with the Twins on a minor league deal and an invitation to spring training. Rivera stayed with the Triple-A Rochester Red Wings for the full 2012 season, batting .226 in 95 games. Rivera was displeased with the Twins when he was passed over and they called up catcher Chris Herrmann from Double-A to add depth in September.

Rivera was signed to a minor league contract by the San Diego Padres on December 12, 2012. He was recalled from the Triple-A Tucson Padres on July 7, 2013, to replace Yasmani Grandal, who was placed on the disabled list. He was hitting .343 with Tucson at the time of his recall. He remained the backup to Nick Hundley for the rest of the season. In 23 games for San Diego, he hit .254/.268/.328 with 7 RBI and 4 runs.

Rivera is married to Mariel Perez, daughter of Eddie 'La Bala' Pérez, a founding member of El Gran Combo de Puerto Rico. She gave birth to twins in September, 2013.

On December 19, 2014, the Padres traded Rivera, Jake Bauers, and Burch Smith to the Tampa Bay Rays in a three-team trade that saw the Rays trade Wil Myers, Jose Castillo and Ryan Hanigan to the Padres, the Padres trade Joe Ross and a player to be named later to the Washington Nationals, and Washington trade Steven Souza and Travis Ott to Tampa Bay. In 2015, he was mainly used as the personal catcher for Chris Archer. Rivera finished the 2015 season hitting .178 with 5 home runs and 26 RBIs. Rivera was released by the Rays on March 30, 2016.

On April 5, 2016, Rivera signed a minor league deal with the New York Mets. He was called up to the major league team on April 26, 2016, when Travis d'Arnaud was placed on the disabled list. He started for the Mets in their Wild Card game against the San Francisco Giants, going 1 for 3 and throwing out Denard Span. Throughout the season he was Noah Syndergaard and Seth Lugo's personal catcher. On December 3, 2016, Rivera and the Mets avoided salary arbitration by agreeing to a one-year, $1.75 million contract.

On August 19, 2017, the Chicago Cubs claimed Rivera off waivers. He was added to the 25 man roster and was the starting catcher for the Cubs the following day against the Toronto Blue Jays.

On January 9, 2018, Rivera signed with the Los Angeles Angels.