The Phillies announced the club received minor league catcher Austin Bossart in the deal. Philadelphia also received cash considerations in the trade.
Vargas, 36, is owed about $2.6 million of his $8 million salary for the remainder of the 2019 season. His contract also includes an $8 million club option for 2020 with a $2 million buyout.
Vargas has a 6-5 record with a 4.01 ERA in 19 games (18 starts) this season. In his last 12 starts, he went 5-3 with a 3.34 ERA.
The Phillies (55-50) trail the first-place Atlanta Braves by 6 1/2 games in the National League East. Philadelphia entered Monday with a 4.59 combined ERA from its starting pitchers, the fifth-worst mark in MLB.