Greinke, a free agent after this season, is 9-3 with a 3.44 ERA this year.
"It should be fun. They are a great team," Greinke said in Milwaukee after the deal was completed. "After the first month of the season, they have been one of the best teams in baseball. There is a lot of talent there. A lot of great players. The pitching staff will be pretty incredible."
Greinke is scheduled to start Sunday against the Tampa Bay Rays.
The Brewers acquired Segura, the Angels' top position-player prospect, along with Double-A pitchers John Hellweg and Ariel Pena. The move further depletes an Angels farm system that was already thin in high-level prospects.
"It shows you that we're trying to win this thing," Angels right fielder Torii Hunter said Friday. "We're trying to win the division, not anything else. We're trying to take this division over, take the crown away from the Rangers."
The trade allows the Angels to upgrade at their most vulnerable position, starting pitching, while holding on to young major leaguers Peter Bourjos and Garrett Richards, both of whom were rumored to be parts of deals in the last few weeks.
Before the trade was completed, Angels manager Mike Scioscia indicated the Angels had a need for pitching. Ervin Santana is 4-10 with a 6.00 ERA and Dan Haren (7-8, 4.76 ERA) missed nearly three weeks with lower-back inflammation.
"No matter how deep your rotation is or how deep your bullpen is, the heartbeat of your club is your rotation and the bullpen has to be able to hold leads," Scioscia said. "So, if you can acquire depth there, you're always looking to do it."
One source with knowledge of Angels general manager Jerry Dipoto's thinking speculated that the Angels might feel they have a good shot at re-signing Greinke this offseason. They will owe him $5.15 million for the remainder of this season.
"I've got to think Jerry thinks he's got a good shot at it," the source said.
Dipoto said he has not initiated conversations about a contract extension with Greinke.
"We'll cross that bridge when we get to it. For the time being, we're thrilled to acquire a player of Zack's caliber," he said. "We're excited to see him get out there and see what kind of difference he can make for the 2012 Angels. We'll worry about the rest later."
Dipoto said the Angels likely will not make any further trades before Tuesday's deadline. Under former general manager Tony Reagins, the Angels were quiet at the deadline last season while watching the Texas Rangers acquired relievers Mike Adams and Koji Uehara.
Then, when the Angels' bullpen was struggling badly in early May, he landed reliever Ernesto Friero from the San Diego Padres in exchange for infielder Alexi Amarista and minor-league pitcher Donn Roach.
Frieri quickly established himself as the Angels' closer, going 11 for 11 in save chances and striking out 51 batters in 29 1/3 innings entering Friday.
The Angels likely will move Santana to the bullpen and decide between Richards and Jerome Williams for their fifth starter.
Hellweg, who has a high-90s mph fastball, is 5-10 with a 3.38 ERA. Pena is 6-6 with a 2.99 ERA.
Greinke started three straight games for the Brewers around the All-Star break -- he was ejected in the first inning of a July 7 game at Houston, started again the next day and then pitched the Brewers' first game after the break.
The Brewers then scrubbed Greinke from his next start, saying the odd stretch of starts had taken him out of his routine and worn him down.
Greinke returned to the mound in Philadelphia on Tuesday, giving up a run and three hits in seven innings -- but the Brewers still found a way to lose the game.
"It was a tough one," Brewers GM Doug Melvin said. "I am very fond of Zack, not only as a player but as a person. He is one of my favorite players that I've ever been associated with. It makes it a little bit tougher. We had to make a decision to turn the page. These three players are players we feel good about. Zack is going to be a great addition for the Angels and help them out. We appreciate everything he did for us. He did all we can ask of him."
Information from ESPNLosAngeles.com's Mark Saxon, ESPN.com senior writer Jayson Stark and The Associated Press was used in this report.