Durbin, 34, will join the Braves in New York on Wednesday.
This spring, Durbin had no record with a 2.35 ERA, allowing four earned runs (eight overall) in 15 1/3 innings with the Nationals, who released him earlier in the week.
The Braves reassigned lefty Yohan Flande to Triple-A Gwinnett to make room on the roster for Durbin. Flande, 26, was 2-0 with a 0.83 ERA in eight appearances with the Braves in the spring.
"Flande had a very good spring and we felt very good with him on the team, but Durbin gives us an experienced guy that knows that role very well and had a very good spring," said Braves general manager Frank Wren prior to the Braves' final exhibition game at Coolray Field. "We watched him a number of times this spring, and we were happy with what we saw."
Originally a third-round pick of the Kansas City Royals in the June 1996 First-Year Player Draft, Durbin has appeared in 364 games, racking up a 38-46 record with four saves and a 5.10 ERA in 12 Major League seasons. He's previously played with the Royals, Cleveland Indians, Arizona Diamondbacks, Detroit Tigers and Philadelphia Phillies. Durbin was 2-2 with a 5.53 ERA in 56 games last season with the Indians.
"I always thought he was a tough at-bat," said Braves third baseman Chipper Jones. "He's able to sink the ball and cut the ball on both sides of the plate, which is always a good thing. A lot of experience, a lot of guile out there on the mound and a guy that can give us some productive innings."
Jon Cooper is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.