Hudson made 21 starts for the Braves in 2013, going 8-7 with a 3.97 ERA. He suffered a broken ankle in late July, which forced him to miss the final two months of the season.
The 38-year-old indicated earlier this year that he would like to return to Atlanta. Hudson has pitched for the Braves since 2005, signing two previous contract extensions with Atlanta after coming over from a trade with the Oakland Athletics before the '05 season.
Starting pitchers Kris Medlen, Julio Teheran, Brandon Beachy and Mike Minor are all under team control next season. Alex Wood bounced between the starting rotation and bullpen in 2013, and could earn a shot in the rotation next year. Atlanta also has a number of pitching prospect that could compete for innings in 2014, including J.R. Graham and David Hale.