Samardzija compiled an 8-13 mark with a 4.34 ERA in 33 starts for the Cubs last season.
The Chicago Tribune reported the deal is worth $5.3 million. It came after Samardzija had filed for $6.2 million and the Cubs countered with $4.4 million.
The team has listened to trade offers for the former Notre Dame wide receiver during the off-season and may yet try to deal him in the absence of a long-term deal, the newspaper said.
Samardzija, 29, has a 29-35 mark record and a 4.19 ERA in 189 appearances (66 starts) in his five-year career, all with the Cubs.
2014: The Year in Music [PHOTOS]