Though details were not disclosed by the club, local media estimate the deal to be worth $68 million over four years.
"It was a priority of ours to get this deal done and keep Alex in a Chiefs uniform long-term," Chiefs general manager John Dorsey said in a statement.
"Alex is a proven leader on and off the field. He is a special individual with a lot of ability, and we are fortunate to have him here."
Smith, 30, who joined the Chiefs in a trade with the San Francisco 49ers in March last year, has gone 30-9-1 as a starter in the NFL since 2011.
The first overall pick by the 49ers in the 2005 NFL Draft, he completed 308 passes for 3,313 yards with 23 touchdowns and only seven interceptions in his first season with the Chiefs.
"Alex is a smart, talented football player that has adapted well to our offensive scheme," said Chiefs head coach Andy Reid.
"He also, obviously, has had a tremendous amount of success as a quarterback in this league. We as a team are very happy to have Alex as our quarterback moving forward."
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Ian Ransom)