Haren's deal is for one year and worth $13 million, Fox Sports reported. The deal is pending a physical, multiple sources say.
Haren, 32, endured a disappointing 2012 with the Los Angeles Angels, going 12-13 with a 4.33 ERA -- the worst of his 10-year career -- in 30 starts. He had his contract bought out by the Angels for $3.5 million in November.
"I think it's a great move, if we can get him," Nationals manager Davey Johnson said Tuesday at the winter meetings in Nashville. "Great athlete, outstanding stuff -- gamer. He fits right in. He can swing the bat. If we get that finalized, he'll be a great addition."
A three-time All-Star, Haren would join a rotation in Washington that includes Stephen Strasburg, Gio Gonzalez, Jordan Zimmermann and Ross Detwiler. That rotation helped carry the Nationals to the NL East title last season.
Johnson said he expects Haren to step in as the leader of Washington's rotation next season.
"I've got some young guys that act like veterans, and they pitched like veterans last year for me," Johnson said. "But adding a veteran like Haren is going to make things even better. I've seen him pitch over the years, and he's an intense competitor. Hopefully we'll get it done."
Haren owns a career record of 119-97 with a 3.66 ERA in 296 games.
Johnson said he's fully familiar with Haren and says he might do even better in the NL.
"He pitched a lot of innings, and he had a decent year for Anaheim," Johnson said. "Also, the American League is a little bit tougher with an extra DH in there. I like his stuff. I like his competitiveness."
Haren has made at least 30 starts in eight straight years. Known for his durability, he went on the disabled list for the first time in his career last season because of a back issue.
Johnson also predicted free-agent first baseman Adam LaRoche will re-sign with the Nationals.
"Adam LaRoche is going to come back," the manager said. "I mean, if I have to go to Kansas and take him and all his cattle to Florida, I will."
Washington brought postseason baseball to the capital for the first time since 1933. After coming within a strike of advancing to the NL championship series on five different pitches, the Nationals lost to St. Louis in Game 5 of the NL division series.
"I think we're in a perfect position to show the world that we're a pretty good ballclub, and we can go farther into the postseason," Johnson said. "World Series or bust, that's probably the slogan this year. But I'm comfortable with that."
ESPN.com's Jerry Crasnick and The Associated Press contributed to this report.