The source said the deal included $5.9 million in guaranteed money.
Chambers led the team in receiving yards (608) and yards per catch (16.9) in nine games in 2009. He also tied Dwayne Bowe for the most receiving touchdowns with four.
Arguably one the team's best acquisitions in 2009, he was a Pro Bowl selection with the Miami Dolphins in 2005.
Chambers has 518 career receptions for 7,435 yards and 57 touchdowns. He was a second-round draft pick for the Dolphins in 2001, and played for the Chargers from 2007-2009 before joining the Chiefs.
Adam Schefter is ESPN's NFL Insider. Information from The Associated Press was used in this report.