The Mavericks will also receive point guard Raymond Felton.
The Knicks will receive Jose Calderon, Samuel Dalembert, Shane Larkin, Wayne Ellington and two second-round picks in the NBA Draft.
Chandler played a vital role in the Mavericks' NBA Championship run in 2011 but then signed a contract worth $60 million over four years with the Knicks. He will make $14.5 million next year.
The trade gives Dallas the defensive presence at center that they have been targeting. They had been interested in signing Pau Gasol and Marcin Gortat in free agency, but with Chandler on board they no longer need to fill that position.
Before signing Dirk Nowitzki to a new contract the Mavericks will have around $26.5 million in cap space. Nowitzki is likely to take a discounted deal to help the team attract free agents, and they should have the room to sign one top-level free agent.
There could be another Knick following Chandler into Dallas. Carmelo Anthony is scheduled to visit with the Mavericks after free agency opens on July 1, as well as the Chicago Bulls and the Houston Rockets.
This is not simply a salary dump by the Knicks. They will free up cap space and pick up some much-needed assets - the two second-rounders will be their only picks in the draft. Calderon is an excellent three-point shooter who will fit perfectly into the triangle offense that is likely to be implemented by new coach Derek Fisher, and Dalembert is not too much of a downgrade at center.
Although Larkin and Ellington saw their playing time in Dallas drop over the course of last season, they will each be expected to make contributions for the Knicks.
In the announcement of the trade, Phil Jackson said: "The journey to build this team for the upcoming season and beyond continues. We have added players with this move that will fit right in to our system while maintaining future flexibility."
Mavericks owner Mark Cuban told ESPNDallas.com: "We think Tyson makes our defense better and we still maintain quite a bit of cap flexibility."
Dallas will hope that flexibility will be used to attract Anthony, or even LeBron James, when free agency begins. No matter how they fair in free agency the team is sure to be better on the defensive end next season with Chandler on board alongside Nowitzki.