The deal is for $210 million with half deferred, according to multiple reports. Scherzer reportedly will receive $15 million annually for 14 years. The deal also includes a record $50 million signing bonus, a person familiar with the negotiations told The Associated Press.
The person said Scherzer is scheduled to take a physical Tuesday, one of the steps needed for the deal to be finalized.
A source had earlier told ESPN.com's Jayson Stark that the Nationals wouldn't have the financial flexibility to sign the right-handed Scherzer unless they have a trade in place to move starter Jordan Zimmermann and possibly shortstop Ian Desmond.
As of Saturday, the source told Stark, the Nationals did not have trades in place for Zimmermann or Desmond.
The Washington Post and CBS earlier reported the deal.
Neither the Nationals nor Scherzer's agent immediately responded to requests by The Associated Press for comment Sunday night.
Scherzer, 30, is a career 91-50 with a 3.58 ERA in seven seasons with Arizona and Detroit. He won the 2013 American League Cy Young Award and has made the All-Star team in each of the past two seasons.
He was 18-5 with a 3.15 ERA in 2014, a year after going 21-3 with a 2.90 ERA and being voted the best pitcher in the American League.
He turned down an offer from Detroit this past March that would have paid him $144 million from 2015-20.
During the winter meetings in San Diego last month, agent Scott Boras gave indications that he was seeking a record payout for Scherzer.
The Dodgers' Clayton Kershaw ($215 million), Detroit's Justin Verlander ($180 million) and Seattle's Felix Hernandez ($175 million) have signed the three biggest deals by starting pitchers in baseball history. But they all agreed to extensions before hitting the open market.
"All the prominent pitchers who've signed were not free-agent players," Boras said in San Diego. "If you put a pitcher like Kershaw into the free-agent market, you're going to get a much different calibration and value. I'm not sure Kershaw's [contract] is relevant.''
Reports from multiple media outlets Sunday said the Boston Red Sox, New York Yankees, Los Angeles Dodgers and the Tigers -- high-profile clubs that have been linked to Scherzer in speculation throughout the winter -- were not among the finalists to sign him.
Scherzer has spent the past five seasons in Detroit after he was traded there by the Arizona Diamondbacks following the 2009 season.
Information from ESPN.com senior writer Jerry Crasnick and The Associated Press was used in this report.