The Senators traded their captain to the Stars on Tuesday for forward Alex Chiasson, forward prospects Alex Guptill and Nicholas Paul and a second-round pick in next year's draft. Dallas also receives forward prospect Ludwig Karlsson.
Spezza, who is set to be an unrestricted free agent next summer, had asked for a trade and general manager Bryan Murray said he would try to accommodate him.
The 31-year-old centre had control of his destination with a limited no-trade clause. Spezza designated 10 teams he would not accept a trade to, which included the Nashville Predators, who had a deal done at this past weekend's draft.
Spezza refused to waive the no-trade clause, leaving Murray to look for other options. Dallas emerged as that option, with the trade being agreed to Tuesday morning before the start of unrestricted free agency.