Succop, taken with the 256th overall pick in last month's NFL draft, played 50 games in four seasons at South Carolina, hitting 71 percent of his field goals with a long of 55 yards. He hit 66 percent his senior season and converted all 30 of his PATs.
The 6-foot-2 Succop worked out with the Chiefs during offseason practices and is expected to compete with second-year kicker Connor Barth for the starting job.
Succop is the first of Kansas City's eight 2009 draft picks to sign. Terms of Tuesday's deal were not disclosed.