Rivero began his playing career at local club Huracán de Treinta y Tres, where despite being a striker he also played as an attacking midfielder. In 2008, he moved to Montevideo to play for Defensor Sporting and remained on the club's youth program for four years. He joined Central Español in 2012, where his professional career began, and debuted for the first team in a game against Danubio. In his first season as a professional he played 16 games as a starter and finished the championship with three goals. For the next championship he was transferred to Rentistas and begins the most successful cycle of his career as the top scorer of the club with 10 goals and is one of the principal figures of the team finishing the season as one of the top scorers of the Uruguayan Clausura 2014 helping Rentistas qualify to the Copa Sudamericana 2014.
His great performances with Rentistas led him to sign for Chilean Champion O'Higgins in 2014, where he scored 10 goals in 16 matches, being one of the best players of the Chilean championship.
Rivero's success at O'Higgins attracted the interest of Vancouver Whitecaps FC of Major League Soccer who signed Rivero as a young designated player on 25 December 2014. He scored his first goal for the Whitecaps on his debut, against Toronto FC, giving Vancouver a 1–0 lead, but they ended up losing the game 3–1. Rivero followed up on his goal with an 86th-minute winner away at Chicago Fire to earn his team a 1–0 win. Rivero continued his impressive goal scoring form to start his Whitecaps career with his third goal in three games, this time another game winner deep into second half stoppage time away at Orlando City SC, again to earn his team a 1–0 win. After scoring three goals in four games, Rivero was named MLS Player of the Month for the month of March 2015. On 4 April, his fifth game with Vancouver, he temporarily took over the leaguelead in goals with four goals in five games after scoring his team's second goal in a 2–0 win over the LA Galaxy. After that Rivero scored another goal against the Columbus Crew SC in a 2–2 draw earning him a league-leading five goals in six games for the Whitecaps. On 6 July 2016, Rivero completed a transfer to Colo-Colo on the same day that the Chilean club's coaching staff resigned.
Santos Laguna
Rivero joined Liga MX team Santos Laguna on a loan in January 2020.
