Phoenix will receive center Michael Handzus, right wing Ladislav Nagy and Jeff Taffe, a Blues' draft pick from last year.
Tkachuk, 28, who served as Phoenix's captain for seven seasons, left the Coyotes' headquarters without talking to reporters.
"It's a sad day for him in many respects," said Bob Murray, Tkachuk's agent. "He has been part of this organization for 10 years and had hoped to remain with the Coyotes for all his years, but he understands the decision had to be made. But St. Louis is a very good organization."
The Blues said Tkachuk would join the team Wednesday night at Minnesota.
"Keith Tkachuk will give our team an entirely new, dynamic personality up front," Blues general manager Larry Pleau said. "Keith is one of only a handful of players in the league who can bring a blend of leadership, physical presence and goal-scoring ability to the rink, shift after shift."
Tkachuk, has 323 goals, 300 assists and 1,508 penalty minutes. In 44 career playoff games, he has 19 goals and nine assists.
This season he registered 29 goals and 42 assists in 68 games. Tkachuk ranks first on the franchise list in penalty minutes and game-winning goals.
Handzus, 24, has been out of the Blues lineup for several weeks after undergoing abdominal surgery. He had 10 goals and 14 assists in 36 games this season. In three seasons, he has 39 goals and 54 assists.
Nagy, 21, had eight goals and eight assists. In 11 games last season, his first, he had two goals and four assists. Previously, he played for Worcester in the AHL.
Taffe, 20, currently plays forward for the University of Minnesota. He represented the United States in the World Junior Championships the last two years.
Simpson, 27, played in 25 games for the Panthers this season, recording a goal and three assists. He returned to the lineup on March 2 after missing 40 games with a concussion.
In six seasons split between Florida and CalgarySimpson has six goals and 35 assists. Last season, his 202 penalty minutes ranked second in the NHL.
Rumors had been swirling for weeks that Phoenix would attempt to move Tkachuk and his $8.3 million contract.
Coyotes GM Cliff Fletcher spoke with several general managers and said the offer would have to be perfect to let Tkachuk go.
The move is part of a string of changes made under new managing partner Wayne Gretzky, who purchased the team along with developer Steve Ellman last month.
On March 5, Phoenix sent goalie Nikolai Khabibulin and defenseman Stan Neckar to the Tampa Bay Lightning for defenseman Paul Mara, forwards Mike Johnson and Ruslan Zainullin and a second-round draft choice.
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