The Nationals claimed him off waivers in a move that will save the Yankees more than $4 million, according to Heyman.
Thornton has a 2.55 ERA in 24.2 innings this season for New York. The 37-year-old lefty has allowed 23 hits and has struck out 20 batters on the year.
Thornton has excelled against left-handed hitters, allowing .556 OPS to the 64 left-handed hitters he's faced this year. The pitcher is due $3.5 million next season.
The Yankees signed left-hander Rich Hill to a major league contract on Tuesday.
- Alex Hampl