Nolan has spent his entire career with the Kings since being drafted in the seventh round (186th overall) in 2009.
The 28-year-old had four goals and four assists in 46 games last season.
His father, Ted, coached the Sabres in two separate stints, the most recent one coming from 2013-15.
“We’re happy to bring Jordan into the mix,” said Sabres general manager Jason Botterill in a release. “His size and speed, along with his experience with such a successful organization like the Kings, make him an asset to the organization.”