The deal is reportedly worth $3 million, more than twice the $1.37 million tender offer Dillon had turned down in June.
The Bengals had been increasing pressure on Dillon in hopes of signing him, after failing to sign him to a multiyear deal. He has rushed for 1,000 yards each of his three NFL seasons with Cincinnati.
Dillon will not be able to reach training camp in Georgetown, Ky., before the Bengals depart Thursday to travel to Atlanta, but he is expected to join the team there.
Coach Bruce Coslet has not decided whether Dillon will play against the Falcons.
"It's great to get Corey in and have him under contract," said Paul H. Brown, the Bengals' vice president who handled the negotiations.
A restricted free agent, Dillon had been threatening to miss the season's first 10 games and play only in the last six so that he could become an unrestricted free agent for next season. That is now moot.
Last week, the Bengals notified Dillon that he would be ineligible to play in the first regular season game on Sept. 10 unless he signed and reported in time for the Atlanta game, which will be the Bengals' second preseason game.
The Bengals had also said Dillon would not be paid for the first regular season game if he did not meet the deadline.
Scott broke two bones in his left leg during practice at the team's training camp in Georgetown, Ky. Smith started only four games last season because of a foot injury and is still learning to run the offense.
Without Dillon, the Bengals had no running back with any appreciable NFL experience.
Dillon already ranks fourth on the Bengals' rushing list with 3,459 yards over the past three seasons. As a rookie in 1997, he rushed for 246 yards against Tennessee to break the single-game rookie record of 237 yards set by Cleveland's Jim Brown against the Los Angeles Rams in 1957.
©2000 The Associated Press. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed