Ríos was drafted in the first round (19th overall) by the Toronto Blue Jays in the 1999 MLB draft. A top prospect in the Blue Jays organization for several years, Ríos had considerable success in the organization's minor league system. In 2003 he hit .352 with 11 home runs and 82 RBIs en route to winning the Double-A Eastern League Most Valuable Player award. Ríos was promoted to Triple-A Syracuse for the start of the 2004 season and made the jump to the big leagues shortly thereafter.
After his participation with the Puerto Rican team in the World Baseball Classic, Ríos began to show why the Blue Jays valued him so highly in his break-out 2006 season. As of June 6, 2006, Ríos was 1st in the league in batting average (among qualified batters) with a .359 average, along with 11 home runs — a new personal best only 60 games into the 2006 season, and 43 RBIs. He then had his first multi-home run game on June 12, 2006, facing the Baltimore Orioles at the Rogers Centre. He was often given as an example of what is known in baseball as a "five-tool player".
In recognition of his outstanding third season in the majors, the young outfielder was rewarded with a spot as a reserve on the American League All-Star Team. While Ríos did not play in the game due to a staph infection in his leg he was invited to attend the All Star Game festivities during the July 10 weekend at PNC Park in Pittsburgh.
Ríos during his tenure with the Blue Jays in 2007 spring training.
Alex said in an interview that he fouled a ball off his foot which resulted in a staph infection and a hospitalization, seriously depleting his strength, and affecting his stats after the 2006 All Star Game.
On February 2, 2007 the Blue Jays and Ríos agreed to a 1-year, $2.535 million contract—meaning that, for at least the next year, the two parties will avoid the process of salary arbitration. Ríos' performance earned him a spot as a reserve on the American League All-Star team and he also agreed to participate in the 2007 State Farm Home Run Derby. He led all competitors by hitting 19 home runs throughout the contest, but the final round was won by Vladimir Guerrero of the Los Angeles Angels of Anaheim.
Ríos fielded the last out in the All-Star game. He led the team in all offensive categories during the first half of the season but slumped after the All-Star Break, with his hitting average settling to slightly below .300, and was overtaken by teammate Frank Thomas as HR and RBI leader . In 2007, he had the lowest range factor of all major league right fielders, 1.82. Ríos was honored with a Fielding Bible Award as the best fielding right fielder in MLB. He was voted the Blue Jays Player of the Year.
Rios signed a seven-year contract with the Blue Jays in April 2008 for a guaranteed amount of $69,835,000: $5.9 million in 2009, $9.7 million in 2010, $12 million each in 2011 and 2012 and $12.5 million each in 2013 and 2014. He finished the 2008 season with a slight statistical decline: .291 average, 15 home runs, 32 stolen bases, and 79 runs batted in. The home run total tied him with Lyle Overbay for the Blue Jays' second most home runs that season (only Vernon Wells had more with 20). Ríos also set a career high in home runs after the All-Star Break that year.
On June 4 against the Los Angeles Angels of Anaheim, Ríos struck out in all five of his plate appearances, also known as the platinum sombrero, in a 6–5 loss to the Angels at Rogers Centre. Later that day Ríos was videotaped cursing a heckling fan after he walked past a child seeking an autograph while leaving a fundraising gala for the Jays Care Foundation. Ríos has since publicly apologized for the incident.
After being claimed off of waivers by the Chicago White Sox on August 10, Rios batted .199, with 3 home runs, 9 RBI and a .296 on-base percentage in 146 at bats over 41 games.
Rios batted .284, with 21 home runs, 88 RBI and a .334 on-base percentage for the White Sox in 2010.
On July 9, 2013, Rios collected 6 hits in a game (tied AL record) in a 11-4 win over the Tigers. Ríos was the starting right fielder for 2013 until his trade. After the trade, Jordan Danks and Avisail García took over. In 109 games for Chicago, he hit .277/.328/.421 with 12 HR, 55 RBI, and 26 SB.
On August 8, 2013, Rios was claimed off waivers by the Texas Rangers, and was traded to them on August 9 for a player to be named later or cash considerations.Leury Garcia was announced as the player to be named later on August 11. He became the team's starting right fielder, replacing the suspended Nelson Cruz. Rios hit for the cycle against the Houston Astros on September 23, 2013. In all of 2013, Ríos hit .278/.324/.432 with 18 HR, 81 RBI and 42 SB.
Rios participated in the 2013 World Baseball Classic playing for Puerto Rico. Although Rios slumped for most of the tournament, he hit a clutch 2-run home run against Japan in the semifinals and handed Puerto Rico its first WBC Finals appearance. They would go on to be defeated by Dominican Republic 3-0 in the finals.