Cowgill and left-handed-hitting infielder Ian Stewart made the Angels' bench, alongside catcher Hank Conger and utility infielder John McDonald.
Right-handers Fernando Salas, Michael Kohn and Matt Shoemaker, and lefty Nick Maronde made the bullpen, joining closer Ernesto Frieri, setup man Joe Smith and middle reliever Kevin Jepsen.
Sent to Triple-A Salt Lake were Shuck, fellow outfielders Brennan Boesch and Matt Long, infielder Grant Green, catcher Luis Martinez, right-handers Cory Rasmus and Brandon Lyon and lefty Jose Alvarez.
Relievers Dane De La Rosa (right forearm inflammation), Sean Burnett (left elbow surgery), Brian Moran (left elbow inflammation) and Ryan Brasier (right elbow strain) will start the season on the disabled list.
Shoemaker is normally a starter, but he made the team thanks to a fantastic spring -- 3.09 ERA, 12 strikeouts and one walk in 11 2/3 innings -- and his ability to temporarily provide length out of the bullpen.
The Angels put their 40-man roster at 39 players by selecting Stewart's contract, and Scioscia likes his versatility.
"He's really a good defender at third base, he's very comfortable at first base and he's played a lot of second base, too, so that versatility will help," Scioscia said. "As far as his swing, you could see as the spring moved on that his swing kept getting better and better and he's really put a charge into balls his last 20 at-bats."
Shuck came out of nowhere to win a job off the Angels' bench last spring, then proceeded to have a very solid rookie season while getting plenty of playing time due to Peter Bourjos' injury. He batted .293 and posted a .331 on-base percentage while leading American League rookies in plate appearances. And he turned in one of the best catches in Angels history, falling into the stands in left field to rob Toronto's Jose Bautista of a home run.
But when the Angels traded Bourjos, it was Kole Calhoun who won the everyday job in right field. And when it was time to make a final decision on the roster, it was Cowgill who won a job off the bench.
Shuck declined to speak to the media upon leaving the Angels' clubhouse.
"Collin has a couple things that gave him the edge over J.B. right now as we start the season," Scioscia said. "One, you talk about the right-handed bat, that's an absolute. I think the other is his versatility in the outfield, being able to play left field and right field is important in a number of areas. Being able to play right field will allow Kole Calhoun the freedom to play first base at any time. It adds depth in many other positions. J.B. was more limited to left field."