The deal, which is pending a physical, was first reported by FanRag Sports.
The 29-year-old right-hander returns to the Pirates after going a combined 12-8 with a 4.17 ERA for Pittsburgh and the New York Yankees last season, when he struck out 127 in 162 innings. He figures to slot in the middle of Pittsburgh's rotation behind Gerrit Cole and Jameson Taillon.
Nova, who missed most of 2014 after Tommy John surgery, followed high-profile relievers Aroldis Chapman and Andrew Miller and outfielder Carlos Beltran out of New York ahead of the August trade deadline.
Nova was 7-6 with a 4.90 ERA in 15 starts and six relief appearances in the Bronx, his inconsistency among the reasons the Yankees struggled for much of the season. He went 5-2 with a 3.06 ERA and three complete games over 11 starts with the Pirates. He also struck out 52 and walked just three.
He was particularly effective at PNC Park, going 3-1 with a 2.45 ERA and giving up just two walks in 40 1/3 innings.
In late September, Nova was on the mound as the Pirates and Chicago Cubs played to the first tie game in the major leagues since 2005 when rain forced the teams to stop in the sixth inning with the score at 1-1. It was the final start of the season for Nova, who limited the World Series-champion Cubs to one run and four hits in 5 1/3 innings.
Information from ESPN's Buster Olney and Jim Bowden and The Associated Press contributed to this report.