Thatcher, 32, has pitched well for the D-backs this year, compiling a 2.63 ERA in 37 games. He has been nearly as effective against righties (.256 batting average against) as lefties (.241).
"Joe did a great job for us," D-backs manager Kirk Gibson said. "I enjoyed my time with him. We wish him well. He's going over to a guy you know I respect in [Angels manager] Mike Scioscia. They're playing well over there and it gives him an opportunity to pitch in even higher-leverage situations. I'm happy for him for that. I'm not happy that he's gone from here, but those things happen."
Thatcher, who will be a free agent after the season, is making $2.375 million this year.
Campana, 28, has had two stints with the D-backs this year, but he was with Triple-A Reno at the time of the trade.
Campana hit .150 in 61 plate appearances for the D-backs this year. While with Reno, he hit .288 and stole eight bases in 10 attempts.
Borenstein, who turns 24 later this month, was ranked as the Angels' ninth-best prospect by MLB.com. He was invited to big league Spring Training and has been at Double-A Arkansas and Triple-A Salt Lake this year.
Named the Angels' 2013 Minor League Player of the Year, Borenstein also garnered the California League's Most Valuable Player Award last year after hitting .337 with 28 homers and 95 RBIs for Class A Inland Empire.
Krehbiel, 21, has made 17 relief appearances for Class A Burlington and Class A Inland Empire this year, compiling a 2.00 ERA to go with five saves.