Kidd, 36, will receive a 3-year, fully guaranteed contract worth in excess of $25 million.
"We are excited to have Jason Kidd back in a Mavs uniform," Mavericks owner Mark Cuban told The Dallas Morning News. "He was a major contributor for us last year, and we expect more of the same next year."
Kidd elected to stay in Dallas in the face of a hard push from the New York Knicks, who last week offered Kidd the most they could ($19 million over three years).
Signing Kidd for more than one season would have impacted the Knicks' efforts to amass substantial salary-cap space for the summer of 2010, when they're expected to woo Cleveland's LeBron James and at least one other top free agent.
Had the Knicks signed Kidd, pressure on Knicks president Donnie Walsh to trade either Eddy Curry or Jared Jeffries -- or both -- would have increased significantly, but sources say that Walsh and Knicks coach Mike D'Antoni felt that acquiring Kidd would have been worth such hassles because of their confidence in Kidd's ability to change the Knicks' culture.
Kidd's interest in returning to the Atlantic Division was mutual, but the Mavericks were always considered favorites to re-sign him because they could comfortably exceed the Knicks' max offer of three years at the projected midlevel exception of $5.8 million per year.
Although Kidd initially sent signals that he planned to take the full holiday weekend before making a decision, Dallas began inching closer to a deal Friday when Kidd and Cuban met at Cuban's house.
Wednesday is the first day teams can formally sign free agents to new contracts after the NBA announces the salary-cap and luxury-tax figures for the 2009-10 season.
Marc Stein is a senior NBA writer for ESPN.com.