Matt Thornton will be a power left-hander out of the Nationals bullpen. (Tony Dejak/Associated Press)

The Nationals’ month-long quest to bolster their bullpen ended Tuesday as they claimed veteran left-hander Matt Thornton off waivers from the New York Yankees, an acquisition that will cost them nothing other than paying Thornton’s salary.

Thornton, 37, has a 2.55 ERA in 46 appearances this season, a span in which the lefty has amassed only 24 2/3 innings. Thornton will make roughly $1 million for the remainder of this season, and he is also under contract for $3.5 million in 2015.

Thornton traveled from New York to Washington late Tuesday afternoon. Williams said it was possible he could be activated for Tuesday night’s game against the Mets, but he did not arrive in time. The Nationals plan to activate him Wednesday.

“He gives us another power option out of the bullpen,” General Manager Mike Rizzo said. “He’s a hard thrower that’s had great success against lefties and righties across his career. He’s got postseason experience, has pitched in the World Series. He’s a former all-star that’s having a terrific year. We think it’s a great addition.”

(Thornton played for the 2013 Red Sox, who won the World Series, but he did not make the postseason roster. In his career, the only playoff series he appeared in is the 2008 American League Division Series. He pitched 3 1/3 scoreless innings for the White Sox against the Rays.)

The Yankees used Thornton, who still throws between 93 and 97 miles per hour, mainly as a left-handed specialist, but Thornton has had success against right-handed batters in his career. This season, right-handers have hit .243 against him with a .704 OPS compared to .250 and .556 against lefties.

“He just adds veteran leadership and veteran presence to the bullpen,” Manager Matt Williams said. “But he can do both roles. He can face righties as well. He’s done that a little bit this year. His times facing right-handers this year are down from normal. But his splits are good. He’s throwing it really well.”

While their  bullpen ranks among the league’s best, the Nationals have sought to augment it throughout July. They nearly acquired a reliever prior to the July 31 non-waiver trade deadline, discussing “countless” relievers, Rizzo said. They heavily scouted lefty Andrew Miller, whom the Red Sox traded to the Orioles. The Nationals continued their search through the waiver process, and they claimed Thornton two days ago, Rizzo said.

The Nationals and Yankees worked through several trade proposals. They discussed the Nationals sending the Yankees a player with the Yankees picking up some of Thornton’s salary. The teams settled on a straight waiver claim.

Either because of fatigue or not, the Nationals’ bullpen has yielded 19 runs in their past 33 1/3 innings. In recent games, Williams has not used certain relievers in order to lessen their workload.

“I think the biggest pressing issue with that is lack of days off,” Williams said. “We were scheduled for one yesterday, it didn’t happen. Games dictate how you pitch guys and what you do, certainly the back of your bullpen. But the lack of days off will push that even further. So, does he help in that regard? Yeah. His innings count is down this year, as compared to his appearances. So he’s fresh. So it’ll do nothing but help, yeah.”

Williams said the Nationals will not move to an eight-man bullpen, which will make three of their relievers left-handed, with Thornton joining Jerry Blevins and Ross Detwiler. Thronton’s skill set seemingly overlaps with Blevins’s. In his past two appearances, Blevins has fired 2 1/3 scoreless innings, but since June 1 he has a 6.05 ERA.

“I don’t think [Blevins’s role] will change,” Williams said. “Jerry’s last two times out have been really good. Strikes to both corners, getting outs, curveball’s really good. So it gives us another option left-handed certainly, with the ability to go a full inning and experience doing so. So does it change anything? Not necessarily. It depends on the day. It depends who pitched the day before, or where we’re at in a series, or who we’re facing, how many lefties they’ve got, all of those things. It just adds to us.”

To make room for Thornton on the 40-man roster, the Nationals moved Taylor Jordan (elbow) to the 60-day disabled list. Jordan recently visited Dr. James Andrews and received tests that revealed only inflammation and no structural damage, Rizzo said. Jordan is 2 1/2 weeks into a six-week program without throwing.

It’s not clear how the Nationals will make room for Thornton on the active roster. The likeliest move would seem to be moving right-hander Blake Treinen back to Class AAA Syracuse.