Jennings tweeted goodbye to Chicago on Thursday.
After catching a flight to New York, Jennings pitched in the Rays' 6-5, 11-inning loss to the Yankees. He contributed to the loss, entering at the start of the eighth and allowing singles to Didi Gregorius and Chase Headley that led to Matt Holliday's run-scoring forceout.
Jennings, 30, is 3-1 with a 3.65 ERA this season. His 49 appearances lead American League lefties and are tied for first among all AL relievers with Cleveland's Bryan Shaw and the Angels' Blake Parker.
"Over the last four weeks, we've seen his stuff kind of tick up," Rays manager Kevin Cash said.
Jennings found out about the trade after the White Sox lost 8-3 to the Chicago Cubs on Wednesday night.
He parked in the garage under his building in the South Loop and was out of cellphone range for five to 10 minutes as he helped his wife, Courtney, who is seven months pregnant, get upstairs along with 3½-year-old daughter Brooklyn. When the phone came to life upstairs, he saw White Sox general manager Rick Hahn had left a text.
The trade added $512,568 of Jennings' $1.4 million salary to the Rays' payroll this season. He is not eligible for free agency until after the 2019 season and lives in Palm Beach Gardens, Florida, during the offseason.
When Jennings walked into the Rays' clubhouse about 2 ½ hours before game time, he saw Logan Morrison walk by and gave his old Miami Marlins teammate, with whom he works out during the offseason, a poke on the arm. Morrison did a double take and gave the pitcher a hug.
Gillaspie, 24, logged a .227/.296/.357 slash line (batting average/on-base percentage/slugging percentage) with nine home runs in 95 games for Tampa's Triple-A Durham farm club. Last year, he led Rays minor leaguers with 18 home runs.
The Associated Press contributed to this report.