Davis is expected to be the closer for the reigning World Series champion Cubs, filling the potential void of free agent Aroldis Chapman. The left-handed fireballer Chapman served as Chicago's closer since a July trade.
Davis posted a 2-1 mark with 27 saves and a 1.87 ERA in 45 appearances last season despite missing nearly the entire month of August due to a forearm strain.
The 31-year-old Davis has been one of the most reliable relievers over the last three seasons, recording a 19-4 mark with 47 saves in 182 2/3 innings. His 1.18 ERA during the last three campaigns is the best among qualified major league relievers.
Davis has a 55-37 career record with 47 saves and a 3.53 ERA in 334 appearances with Tampa Bay and Kansas City.
"He's an All-Star closer, he's closed out world championships," Cubs general manager Jed Hoyer said. "One thing we learned this year -- when you play that extra month, it's hard on your bullpen. Wade can pitch the ninth. But we really like the other guys that we have. Hopefully this can take the burden off all of them."
Soler batted .238 with 12 homers and 36 RBIs in 86 games last season. The 24-year-old Cuban is batting .258 with 27 homers and 98 RBIs in three campaigns with the Cubs.
"We love his upside -- love his power," Royals general manager Dayton Moore said Wednesday. "The fact that we have the DH (in the American League) we can utilize him in both spots."