Chandler was the Mavericks' starting centre during their NBA championship run three years ago, averaging eight points and 9.2 rebounds per game as Dallas claimed its first title in franchise history by beating Miami in six games.
While guard Raymond Felton also joins Chandler in Dallas, the Knicks received point guard Jose Calderon, veteran centre Samuel Dalembert, guards Wayne Ellington and Shane Larkin as well as the Mavericks' two second-round picks in the NBA entry draft.
It's the first major move for New York under new team president Phil Jackson. It also comes just two days after star forward Carmelo Anthony opted out of his contract, deciding to test the free agent market.
"The journey to build this team for the upcoming season and beyond continues," Jackson said. "We have added players with this move that will fit right into our system while maintaining future flexibility.
"We would like to thank Raymond and Tyson for their time and hard work with the organization over the past few years."
The Knicks acquired Chandler from the Mavericks in a three-team deal in December 2011. He signed a four-year deal with New York and was named the NBA Defensive Player of the Year in 2012.
Chandler, 31, was one of several key players that Dallas let go after their championship run.
The 12-year veteran won a gold medal with the USA in the 2012 London Olympics. He played just 55 games last season due to injuries.
Felton is coming off a disappointing season with the Knicks that included an arrest on weapons charges in February.
While Spain's Calderon and centre Dalembert were both starters for the Mavericks, Larkin is a promising young point guard and a first round draft pick in 2013. The Knicks also get the 34th and 51st picks in Thursday's draft.
Before the trade, the Knicks did not have any picks in the draft.
The 32-year-old Calderon has career averages of 10.2 points and 6.8 assists in 634 NBA games. He established a single-season league record by shooting 98.1 percent from the free-throw line in 2008-09 with the Toronto Raptors.
Calderon helped Spain to silver medals at the 2008 Beijing Games and the London Games.
Dalembert is best known for his defensive skills. He spent just one season with Dallas after joining the team as a free agent last July.
The 2.11 metre (6-foot-11) journeyman averaged 6.6 points and 6.8 rebounds while starting 68-of-80 games and, like Chandler, will be an unrestricted free agent following this season.