Trumbo, who belted 34 homers and drove in 100 runs while batting .234 last season for the Angels, went to Arizona. Diamondbacks outfielder Adam Eaton was sent to the Chicago White Sox.
Also as part of the deal completed at baseball's winter meetings, the Angels acquired left-handed pitchers Tyler Skaggs from Arizona and Hector Santiago from the White Sox.
The D-Backs also acquired one minor-league prospect each from the Angels and White Sox.
Skaggs, 22, was the key player in the trade for Los Angeles. He originally selected by the Angels in first round of the 2009 amateur draft but was dealt to Arizona in a trade for pitcher Dan Haren.
Skaggs has a 3-6 mark and 5.43 ERA in 13 major league starts.
The White Sox, meanwhile, landed Eaton, 25, who batted .252 with 10 doubles, three homers and 22 RBI over 66 games with the D-Backs last season.