He played in Major League Baseball (MLB) for the Seattle Mariners from 2009 to 2012, New York Yankees from 2013 to 2014, San Diego Padres in 2015, Washington Nationals from 2016 to 2018, the Oakland Athletics in 2018 and the Texas Rangers in 2019.

As a pitcher for the school's baseball team, Kelley went 9–1 with a 1.12 earned run average (ERA), and 95 strikeouts in 74 innings pitched.

He was then promoted to the Mavericks where in 12 relief appearances he was involved in no decisions, gave-up no earned runs, saved three games, and struck-out 12.

[14] Kelley made his major league debut on April 10 against the Oakland Athletics and struck out two in one inning pitched.

[17] As a result, the Mariners called up pitcher Garrett Olson from the Triple-A Tacoma Rainiers to replace Kelley on the 25-man roster.

On June 3, the Mariners' activated Kelley from the disabled list, and as a result optioned first baseman Mike Carp to Triple-A Tacoma.

On February 24, 2010, during spring training workouts, Kelley was injured after he was accidentally kicked in the chin by teammate Mark Lowe.

On April 30, after pitcher Cliff Lee was activated from the disabled list, the Mariners optioned Kelley to the Triple-A Tacoma Rainiers.

[23] On May 5, 2014, Kelley was ejected for the first time in his MLB career by home plate umpire Laz Díaz for arguing balls and strikes.

[26][27] On December 29, 2014, he was traded to the San Diego Padres in exchange for minor league pitcher Johnny Barbato.

[30] Ticketed as the Nationals' primary setup man, Kelley filled in as closer while Jonathan Papelbon was on the disabled list in June 2016.

[31] Kelley generally excelled in the role of setup man, but he surrendered the runs that ultimately ended the Nationals' year, with Los Angeles Dodgers third baseman Justin Turner hitting an RBI triple to deep center field in Game 5 of the 2016 National League Division Series.

[33] Kelley experienced dramatic increases in his rates of walks and home runs allowed over the first half of the season,[34] landing on the disabled list twice (with a lower back strain in May and a right trapezius strain in June) as he struggled to a 7.00 ERA and 4.5 home run rate per nine innings.

[35] Those tendencies continued after he returned from the disabled list; by the time he suffered a season-ending elbow injury on September 22, he had allowed 12 home runs in 26 innings at the major league level and finished the year with a 7.27 ERA.

[36] While still struggling with his home run rate and injury issues, Kelley enjoyed a rebound performance over the first half of the 2018 season, pitching to a 3.34 ERA through the month of July.

[37] On July 31, 2018, Kelley was called to pitch the ninth inning with the Nationals holding a 25–1 lead over the New York Mets.

After allowing a two-run home run to Austin Jackson, Kelley angrily threw his glove to the ground and glared into the Nationals' dugout.