David Pepe, Nathan's agent, declined to comment on the original report by Foxsports.com.
The pending deal comes after Brian Wilson, who had also been in negotiations with the club, broke off talks with Detroit to explore other opportunities, a baseball source told Jerry Crasnick of ESPN.com.
Nathan, 39, is tied with Rollie Fingers for 10th place on baseball's career list with 341 saves. He went 6-2 with a 1.39 ERA and 43 saves and made his sixth All-Star team with the Texas Rangers in 2013.
Detroit general manager Dave Dombrowski made upgrading the bullpen an offseason priority after the Tigers' relief corps struggled in the American League Championship loss to Boston. Nathan takes over at closer for Joaquin Benoit, who filed for free agency after notching 24 saves in 2013.
The Tigers traded starter Doug Fister to Washington on Monday, and will move Drew Smyly from the bullpen to the rotation in 2014. Left-hander Ian Krol, who went 2-1 with a 3.95 ERA in 32 appearances with the Nationals, will try to pick up some of the slack created by Smyly's transition to starting.
Nathan made the All-Star team both seasons with Texas after signing a two-year deal following the 2011 season, his first after Tommy John surgery forced him to miss the 2010 season.
Nathan wanted to prove he could close again, and he did that with Texas. Because he reached 55 appearances, he had the right to void the final year of his contract, which would have paid him $9 million had the Rangers decided to exercise it and keep him.
Buster Olney and Jerry Crasnick of ESPN.com and Richard Durrett of ESPNDallas.com contributed to this report.