Career
He previously played for the Atlanta Braves. Atlanta Braves
Avilán signed with the Atlanta Braves as an international free agent in 2008. The Braves added him to their 40 man roster after the 2011 season to protect him from the Rule 5 draft.
On July 5, 2012, Avilán was called up by the Braves to replace the injured Jonny Venters.
He made his first appearance on July 14 against the New York Mets, striking out the only batter he faced. Avilán made 75 appearances in 2013, posting a 1.52 earned run average with a.144 batting average against and.219 on base percentage.
In addition, he made appearances in all four games of the 2013 NLDS. However, he struggled through the first half of the 2014 season, recording a 4.85 European Research Area in 47 games. Avilán was demoted to Triple A Gwinnett on July 19, 2014 and replaced by Chasen Shreve.
He would finish the 2014 season with a 4.57 European Research Area in 62 games.
2015 was kinder to Avilán in a Braves uniform, as in 50 appearances, he posted a 3.58 European Research Area with a 1.20 WHIP. Los Angeles Dodgers
On July 30, 2015, in a three-team trade, the Los Angeles Dodgers acquired Avilán, Mat Latos, Michael Morse, Bronson Arroyo, Alex Wood, Jim Johnson, and José Peraza, while the Miami Marlins acquired minor league pitchers Victor Araujo, Jeff Brigham, and Kevin Guzman, and the Braves received Héctor Olivera, Paco Rodriguez, minor league pitcher Zachary Bird and a competitive balance draft pick for the 2016 MLB Draft. He pitched in 23 games for the Dodgers with a 5.17 European Research Area. At the conclusion of the season, the Dodgers signed him to a one-year, $1.39 million, contract to avoid salary arbitration.