The deal is pending a physical.
The Nationals issued a "media alert," saying that they would hold a news conference at their stadium on Tuesday to announce a free-agent signing. The team did not identify the player in the release.
The 31-year-old Marquis is a right-hander who went 15-13 with a 4.04 ERA and 115 strikeouts in 216 innings for the Colorado Rockies in 2009. He made the NL All-Star team last season, thanks to an 11-6 record and 3.65 ERA at that point. But Marquis fizzled down the stretch and wasn't part of the Rockies' postseason starting rotation.
Still, he brings the sort of veteran, innings-eating presence that Washington's starting rotation has been lacking.
Marquis made at least 32 starts in five of the past six seasons; the lone exception was 2008, when he started 28 games for the Cubs.
Only one pitcher, left-hander John Lannan, made 20 or more starts for Washington last season, when the club finished with the worst record in the majors, 59-103. It was the second consecutive year that the Nationals lost more than 100 games.
The addition of Marquis represents a building block and a step toward fixing one of the Nationals' most glaring weaknesses: starting pitching. He's also the club's biggest move of the offseason so far, following the signing of free-agent catcher Ivan Rodriguez to a $6 million, two-year deal, and a trade with the New York Yankees for relief pitcher Brian Bruney.
Because Marquis was a Type B free agent and was offered arbitration by the Rockies, Colorado stands to receive a compensatory pick between the first and second rounds in June's amateur draft.
ESPN The Magazine's Buster Oleny and The Associated Press contributed to this report.