Shields, Davis and a player to be named later went to the Royals late Sunday in exchange for outfield prospect Wil Myers, pitchers Jake Odorizzi and Mike Montgomery and third baseman Patrick Leonard.
Shields, soon to be 31, has compiled an 87-73 mark over seven seasons in Tampa. He is also the Rays' all-time leader in starts (217), innings pitched (1,454 2/3), strikeouts (1,250), complete games (19) and shutouts (eight).
Last season was a good one for the right-hander. He finished with a 15-10 record and an ERA of 3.52.
Davis was converted from a starter to a reliever last season and posted a 3-0 record with a 2.43 ERA in 54 appearances, but is expected to again be used a starter for the Royals.
Myers, 22, batted .303 with 24 home runs and 79 RBI in 99 games this past season for Kansas City's Class AAA affiliate in Omaha.