The agreement ended the possibility of a long holdout by the fifth overall pick in April's draft.
"We're pleased to announce the signing of the first of our two number one draft choices," said Chiefs President Carl Peterson. "Even though it took a little longer than we had hoped, Glenn has missed only a couple of walk-through practices and we expect he'll be involved very quickly."
The 6-foot-2, 316-pound Dorsey had been regarded as a possible No. 1 pick but Miami took Michigan offensive tackle Jake Long. Dorsey, a first-team all-America selection fell to No. 5.
Dorsey had 69 tackles and seven sacks in 14 games for LSU last season. In 51 career games (30 starts) for the Tigers, Dorsey had 179 tackles, 13 sacks and 27 tackles for loss.