The deal is worth $3.5 million, according to multiple media reports.
Byron, who has eight goals and three assists, was acquired from the Calgary Flames before this season and was slated to become an unrestricted free agent in July.
The 26-year-old center has 25 career goals and 59 points since Buffalo selected him in the sixth round of the 2007 NHL draft.
"We are pleased to have reached an agreement with Paul Byron," Bergevin said in a statement. "A fast-skating and versatile forward, Paul has been an important addition to our team. He can contribute on the offensive side while being responsible defensively. Furthermore, he demonstrates an exemplary attitude and the qualities of a true professional. We're proud to have him among our group of forwards for the next three seasons."