Maddux became a free agent after last season, then accepted the Braves' offer of arbitration in December. He had asked for $16 million, the highest amount ever submitted in arbitration, and the Braves had offered $13.5 million.
A hearing had been scheduled for Thursday in St. Petersburg.
The previous record for a one-year contract was pitcher David Cone's $12 million deal with the New York Yankees in 2000.
"We're delighted this issue is resolved and that we can now focus on his stature as a pitcher and his production for our team," Braves general manager John Schuerholz said.
Maddux, 37 in April, went 16-6 with a 2.62 ERA last season. He tied Cy Young as the only pitchers in baseball history to win at least 15 games in 15 consecutive seasons.
In 2002, Maddux made $13.1 million in the final season of a $57.5 million, five-year contract.
If Maddux's case had gone to a hearing, win or lose he would have broken the arbitration record, set by outfielder Andruw Jones when he beat the Braves two years ago.
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