The deal is worth $20 million, ESPN The Magazine's Buster Olney is reporting. It could be announced as early as Thursday, according to multiple reports.
"I wanted to play for a contender, and opportunities weren't exactly what I wanted them to be," Dunn told MLB Network. "But I get a chance now to go and hopefully turn a program around."
Dunn, 29, hit .236 with 40 home runs and 100 RBIs with the Arizona Diamondbacks and Cincinnati Reds last season.
Dunn has hit at least 40 home runs each of the past five seasons. In 1,131 games, Dunn has 278 home runs.
The 2008 Nationals hit 117 homers as a team -- ranking 15th of 16 NL teams -- while finishing with the worst record in the major leagues at 59-102.
"He's an obvious power hitter and someone who can hit in the middle of the order, drive guys in, hit home runs," Zimmerman said by telephone from Florida. "He's something that we haven't really had consistently. It's exciting, and it makes us better."
After pursuing first baseman Mark Teixeira until he signed with the Yankees, the Nationals had not managed to add a slugger or make a truly significant offseason move -- until now.
The 29-year-old Dunn, who can play the outfield or first base and is a left-handed batter, has a .247 average with 278 homers and 672 RBIs over his career. The 6-foot-6, 240-pound Dunn also has a .381 on-base percentage and last year led the NL in walks with 122.
It's the latest example of Nationals general manager Jim Bowden bringing one of his former Cincinnati Reds players to Washington, a list that includes Kearns, Ryan Wagner, Aaron Boone, Wily Mo Pena and Dmitri Young. When he was the Reds' GM, Bowden drafted Dunn in the second round of the 1998 amateur draft.
"We started something in 1998, me and Austin and Jim, and we never got to see it out," Dunn said. "And hopefully now ... we can somehow jump-start this team."
Asked why his once and future teammate chose to come to Washington as a free agent, Kearns said: "He knows Jim. He has a relationship with Jim."
Neither Bowden nor president Stan Kasten responded to requests for comment.
Information from The Associated Press was used in this report.