The Braves also get $2.5 million, while the Angels get minor league catcher Jose Briceno in a deal headlined by two quality major league shortstops trading places on teams with differing needs.
Simmons is arguably the best defensive shortstop in baseball, winning the Gold Glove in 2013 and 2014. He was named the Wilson Defensive Player of the Year on Wednesday, offsetting his mediocre offensive skills with spectacular work in the field.
Simmons also is under contract through 2020, while Aybar could become a free agent next winter.
"We are extremely excited to acquire an impact shortstop and one that fits our championship standards," Angels general manager Billy Eppler said in a statement. "Andrelton provides us up-the-middle foundation at a premium position for years to come. To know we have a player with Andrelton's talents, drive and competitiveness at such a young age signed through 2020 is a vital step in adding to our core group."
Coming off a 97-loss season, the Braves got an offer they couldn't pass up, according to new general manager John Coppolella, who dealt away one of the team's most popular players in his first trade since his promotion.
"We need more talent," Coppolella said. "We think all three players in the trade will have an impact on our major league team for the 2016 season."
Over that past year, the Braves have undergone a massive rebuilding job, loading up on pitching prospects and trying to set their team for a return to playoff contention when they move into a new suburban stadium in 2017.
But Coppolella insisted this deal wasn't entirely geared to the future. Aybar should be an upgrade offensively over Simmons, no small consideration given Atlanta's feeble offense. Also, the glut of young pitchers gives the Braves a chance to pursue future deals to upgrade the offense.
"You can make an argument that we'll win more games with Aybar," Coppolella said. "This wasn't a prospect trade. This was a value-for-value trade with two really good prospects in it."
Aybar has been the Angels' starting shortstop since 2008 and a key player in Anaheim for a decade, making the AL All-Star team in 2014 while batting .276 in 1,220 regular-season games since 2006. He has been dependable in the field and at the plate, although his offensive contributions slipped slightly last season to his lowest average (.270) and RBI total (44) in a half-decade.
"This is one of those transactions where each organization will benefit in both the short and long term," Eppler said.
Los Angeles broke up its long-standing double-play combination last season by trading second baseman Howie Kendrick to the Dodgers one year before his own free agency.
With no clear heir to Aybar in the Angels' system beyond long-term Cuban prospect Roberto Baldoquin, the Angels' new general manager gave up his two top pitching prospects to land a long-term replacement and another defensive star to play with Mike Trout and Gold Glove winner Kole Calhoun.
The 6-foot-2 Simmons has a career .983 fielding percentage with outstanding range, leading all major leaguers since 2013 with 1,354 assists and leading all shortstops with 692 putouts.
He is under the big-budget Angels' control for the next five seasons at a fairly hefty price, making $11 million in 2018, $13 million in 2019 and $15 million in 2020.
On the other hand, Simmons batted .265 with four homers and 44 RBIs last season, showing little progress at the plate. He had 17 homers and 59 RBIs in 2013, his first full season in the major leagues.
Newcomb, the 15th overall pick in the 2014 draft, was considered the top prospect in the Angels' thin minor league system. The 6-foot-5 left-hander moved up to Double-A Arkansas last season, and is expected to be in a big league rotation soon.
Ellis is a promising right-hander who also pitched at Arkansas last season.
Coppolella mentioned David Price when talking about Newcomb.
"Obviously, there are areas in which he can improve," Coppolella said of the youngster. "But we think he can pitch at the very top of a rotation."
AP Sports Writer Paul Newberry in Atlanta contributed to this report.