Brad Lidge reacts after the Phillies’ victory in Game 5 of the 2008 World Series. (Chris O'Meara/AP)

The Washington Nationals agreed to terms with veteran right-handed reliever Brad Lidge on a one-year deal Thursday, adding depth and leadership to a bullpen already considered one of the best in baseball. After four seasons with the Philadelphia Phillies, Lidge will provide the Nationals with a devastating slider and mountains of experience, including recording the final out of the 2008 World Series.

Lidge, who has 223 saves over 10 major league seasons, will join Tyler Clippard and Henry Rodriguez as setup relievers for closer Drew Storen, who in the past has cited Lidge as a role model. Though he’s spent the majority of his career as a closer, Lidge signed with the Nationals with the understanding he would pitch before the ninth inning.

“Washington has a closer, and he knows that,” said Rex Gary, Lidge’s agent. “He’s coming in to pitch late innings and important situations. He’s fully aware that the game plan is to use him in the setup role.”

Lidge signed for $1 million, plus incentives based on appearances and games finished. He felt at ease with the Nationals’ direction and his place on the team. General Manager Mike Rizzo knew Lidge in the late ’90s, when he was an amateur scout and Lidge played at Notre Dame.

“I’ve got to give Mike Rizzo credit,” Gary said. “When the Nats got into this thing and started looking at the possibilities, Mike Rizzo was relentless. He made an offer quickly, things progressed quickly. He made Brad feel really comfortable, encouraged about what the opportunities would be.”

The Nationals already had plenty of talent and depth in their bullpen, which last season ranked fifth in the majors with a 3.20 ERA. But Rizzo wanted to add a veteran to a young mix — Storen, Clippard and Rodriguez are all 26 or younger.

“He’s obviously an incredible pitcher,” Storen said. “As a resource, he’s going to be somebody who, I’ll obviously pick his brain quite a bit. I’ll ask him a million questions. He’s been there. He’s thrown that last pitch of the World Series. It’s going to be a lot of fun.”

Said Nationals outfielder Jayson Werth, who played with Lidge in Philadelphia: “Brad is one of the more interesting teammates I’ve had. Not your average athlete. Very intelligent on and off the field. He will bring culture to our clubhouse, along with his nasty slider. ”

Lidge, 35, missed the first two months of last season recovering from a torn rotator cuff, which limited him to 25 games. The effects of the injury dropped his average fastball velocity to 89 mph, down from roughly 96 at its peak in 2007 and 2008.

Still, in the 19 innings he pitched in 2011, despite his limitations, Lidge was highly effective. He allowed three earned runs and, an ERA of 1.40. And he struck out 10.7 batters per nine innings; for context, that’s a shade better than Clippard.

A healthy Lidge gives the Nationals one of the deepest bullpens in the majors. Paired with a rotation topped by Stephen Strasburg, Gio Gonzalez and Jordan Zimmermann, the Nationals’ pitching staff could compare to the best in baseball.

“It’s pretty unbelievable,” Storen said. “You look at the way that teams played against teams like the Braves. Hitters know that if they’re going to strike, they need to do it against our starters. And with the way our rotation is shaping up, they’re not to go get much from them, either.”