The deal is pending a physical, the source told Crasnick. The deal was first reported Friday by Yahoo! Sports.
The 23-year-old Ventura went 14-10 with a 3.20 ERA last year in his rookie season, including a seven-inning scoreless performance in beating the San Francisco Giants in Game 6 of the World Series.
The right-hander signed a one-year deal worth $535,675 for the 2015 season on March 3.
In his March 27 spring training start against the Seattle Mariners, Ventura threw seven no-hit innings, striking out four and walking two before being lifted on a pitch count.
ESPN.com recently ranked Ventura as No. 75 in the BBTN 100. With James Shields leaving in free agency, Ventura anchors a projected starting rotation that includes Danny Duffy, Edinson Volquez, Jeremy Guthrie and Jason Vargas.