Sources told MLB Network that the deal is for two years and $19 million.
Sanchez, 34, posted a 2.83 ERA and a 7-6 record in 25 games last season for the Atlanta Braves. The 13-year veteran signed with the Braves in free agency last offseason.
The 2013 ERA title winner owns a career 3.99 mark while pitching for the Florida Marlins, Detroit Tigers and Braves. Sanchez is 97-100 as a starter and has appeared in 309 games.
The Nationals had a 4.04 ERA last season, ranking No. 15 in baseball among pitching staffs.