Irving, 25, requested a trade during a July meeting with Cavaliers owner Dan Gilbert. At the time, Irving said he wanted to play in a situation where he can be more of a focal point and that he no longer wanted to play alongside LeBron James, sources said.
"This has obviously been a roller coaster of a day for us, trading away Isaiah and Jae and Ante, especially Isaiah and Jae who have been such big part of our team and our success and our Celtic culture as leaders of our team. Very, very difficult day," said Celtics president of basketball operations Danny Ainge. "At the same time, a very exciting time [to add] one of the best offensive players in the league."
Ainge said that it was a very tough phone call to inform Thomas, who had emerged as the face of the franchise since arriving at the trade deadline in February 2015.
Ainge also said the Celtics did their homework on Irving after his falling out with LeBron James in Cleveland and said the player was "excited" to be joining the Celtics. He acknowledged that Irving's price tag was high.
"It is a high price tag," he said. "But acquiring a 25-year-old perennial All-Star, a player that fits a timeline for us, and is a fantastic offensive player, one of the best offensive players in the league, you have to pay a heavy price."
Pressed on the difficulty of giving up the unprotected Brooklyn pick, Ainge noted, "We valued it from the time we got it and it's still very valuable. Obviously, we value Kyrie more. It's that simple."
Irving has three years and $60 million left on his contract, but he can opt out of the final year before the 2019-20 season.
Thomas, 28, led the Celtics to the best record in the Eastern Conference last season, averaging 28.9 points and 5.9 assists over 33.8 minutes per game during the regular season.
Thomas has spent the offseason recovering from a right hip injury that kept him out of the final three games of the Eastern Conference finals. He opted not to have surgery.
Ainge said Thomas' injury did play "some" into him making the deal. Celtics coach Brad Stevens said Monday that he was not sure Thomas would be ready for the start of training camp.
Thomas will become a free agent when his contract expires at the end of June. He has said he believes he's worthy of a maximum contract.
Sources told ESPN that Cleveland has no short term concerns on Thomas' health and that they feel they are getting a motivated All-Star in a contract year.
Crowder has been a core piece of the Celtics' resurgence. A solid perimeter defender, the 27-year-old forward averaged 13.9 points and 5.8 rebounds last season. He also has one the friendliest cap numbers in the NBA -- $6.8 million, $7.3 million and $7.8 million. He does not become a free agent until the summer of 2020.
Zizic was the Celtics' first-round pick in 2016, the 23rd overall. He's a highly regarded 20-year-old out of Croatia described by ESPN's Fran Fraschilla as "one of my favorite kids in this draft. He's 6-11, 240. He has a mean streak." In addition to his tremendous upside, Zizic was also included for salary purposes.
Irving waived a $5.8 million trade kicker --15 percent of total money remaining on his Cleveland deal, to join Boston, sources said.
When asked for LeBron James' reaction to the deal, a source close to James told ESPN, "LeBron will be ready at training camp no matter what."
The trade will give Cleveland $29.1 million in tax savings. Cleveland's tax is now $49.3 million, down from $78.4 million.
The Celtics and Cavaliers open the season in Cleveland on Oct. 17.
Opening night should be interesting," an unnamed Cavs player told ESPN.
