The deal is worth nearly $12 million and includes escalators that could reach $14 million, a source who has spoken with Floyd told NFL.com and NFL Network's Ian Rapoport.
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Floyd has 13 catches for 227 yards and one touchdown in three games this season. The 6-foot-5, 225-pound former Wyoming player has 190 receptions for 3,397 yards and 21 touchdowns in eight NFL seasons.
"I guess all these years of hard work have paid off," Floyd said in an interview posted on the team's official website. "They took great care of me, and now I get to start and finish my career as a Chargers. That's something I always dreamed about."
"That's the goal," Gaither said. "This was a big day, a major hurdle to my return. It felt good to be out there, and I'm going to keep on working and try to help this team in a game as soon as humanly possible."
That might come the following week in New Orleans.
The Associated Press contributed to this report.