The deal also includes a club option for 2023 for an additional $13 million. According to ESPN's Jeff Passan, the deal includes a buyout that will pay Smith $1 million if the Braves do not pick up that option.
Smith, 30, earned 34 saves in 38 opportunities for the San Francisco Giants last year while going 6-0 with a 2.76 ERA.
A Georgia native, Smith struck out 96 while walking 21 and was named to the All-Star team for the first time in his career.
Smith had received a $17.8 million qualifying offer from the Giants and he signed with the Braves shortly before the deadline to accept that offer. Atlanta will now forfeit its second-highest pick in the 2020 draft for signing Smith.
Melancon, who was acquired by the Braves from the Giants at the trading deadline last season, reacted on Twitter to Atlanta signing his former teammate.
We just got even better. Counting down to February.— Mark Melancon (@Mark_Melancon_) November 14, 2019
Melancon saved 11 games for the Braves down the stretch last season. It is unclear whether the Braves plan to keep him in the role or have Smith become the team's primary closer in 2020.
The Associated Press contributed to this report.