Strop joined the Rangers for the series finale at Yankee Stadium, hoping to make his major league debut.
Jennings is 2-4 with a 4.13 ERA in his first season as a reliever. He made 44 appearances this year and pitched a team-high 61 innings in a variety of relief roles.
Jennings had a 3.26 ERA at the All-Star break but had struggled since then with a 7.07 ERA. He gave up three runs and three hits in one inning Wednesday night in a 9-2 loss to New York, and the Rangers weren't sure he would regain his earlier form.
Texas designated him for assignment before putting him on outright release waivers. Jennings is 62-74 with a 4.95 ERA lifetime with Colorado, Houston and two years in Texas.
Strop was 6-6 with five saves and a 5.06 ERA with Oklahoma City and Double-A Frisco. Texas signed him last year after he was released by Colorado. Formerly an infielder, the 24-year-old Strop is in his second full season as a pitcher.
The Rangers purchased his contract from Triple-A.