McGraw, a key special-teams player, will be entering his third season with Kansas City and his eighth NFL season.
The Chiefs also signed linebacker Darrell Robertson, who was on New England's practice squad last season. He had 11.5 sacks during his collegiate career at Georgia Tech and he will have a chance to make the Chiefs' roster. The team is in dire need of pass-rushers.
The Chiefs still have plenty of salary-cap room remaining and are considering several free agents, particularly on defense.
Meanwhile, former Chiefs quarterback Damon Huard had some interesting things to say during a Seattle radio interview. Huard, who the Chiefs did not want to bring back, signed with San Francisco this week.