Jenings, 27, has 116 appearances, all in relief, over the last three seasons for the Marlins. While posting a 1.34 ERA over 47 appearances this past season, he went 19 consecutive appearances at one point without giving up an earned run.
The 6-foot-3, 201-pounder was a ninth-round selection by Miami in 2008 out of Nebraska.
Rienzo, 26, made 21 starts for the White Sox over the past two seasons. He went 4-5 with a 6.82 ERA in 18 appearances (11 starts) this past season.