Nathan, 42, requested to be released when he wasn't recalled to the majors before Thursday.
The Nationals released Nathan after spring training, but the right-hander later signed a minor league contract with the club that included a June 1 opt-out clause.
Nathan struggled for the Nats' Triple-A club in Syracuse, posting a 6.19 ERA in 16 innings. He was 0-2 with four saves.
He has had two Tommy John surgeries in his career, most recently in 2015, when he was with the Detroit Tigers.
His 377 career saves rank second among active pitchers and eighth in major league history.
In 16 major league seasons, Nathan has posted a 2.87 ERA and 64-34 record in 923 1/3 innings.