The trade announced Sunday reunites Upton with his younger brother, Justin, who was obtained by the Padres in one of several trades made by the team during a December makeover. Justin Upton is San Diego's starting left fielder.
The Padres had a glut of outfielders after acquiring Matt Kemp, Justin Upton and Wil Myers.
Kimbrel has had at least 42 saves in each of the last four seasons.
Corey Kluber, the American League
"I wanted to be here. I wanted to be in Cleveland," said Kluber, who was 18-9 last season. "That was the driving force behind it for me."