A press conference to announce the signing reportedly will be held Tuesday.
The deal includes deferrals and "rolling" opt-out clauses after the third and fourth seasons, per Jon Heyman of MLB Network. Strasburg can also earn up to $1 million in bonuses each year, which could increase the total value of the contract to $182 million, according to Heyman.
Strasburg, 27, was the first overall pick in the 2009 amateur draft. The 6-foot-4 right-hander is 59-37 with a career 3.06 ERA and 948 strikeouts in 818 2/3 innings over seven seasons with the Nationals. He was an All-Star in 2012 and finished ninth in Cy Young Award voting in 2014.
This season, Strasburg is 5-0 with a 2.36 ERA (42 innings) and 47 strikeouts in six starts.