The five-year contract is worth $15.85 million ($18.5 million max) with $9.6 million guaranteed, according to the Cincinnati Enquirer.
Gresham, the 21st overall pick, signed his deal Tuesday, then put on his No. 84 jersey and jogged onto the field for an afternoon practice six minutes after the rest of his teammates on offense got started.
The former Oklahoma star missed eight practices, but has plenty of time to win the starting job.
The Bengals open their preseason next Sunday in the annual Hall of Fame game in Canton, Ohio, against the Dallas Cowboys. Coach Marvin Lewis said after Monday night's practice that Gresham could play in the first of Cincinnati's five preseason games.
"We'll get him in here, get him going and he'll have an opportunity to get into the football game on Sunday," Lewis said on Monday. "He has a chance to get off to a great start. He'll get four good weeks of football and be ready for that first week [of the regular season]."
Gresham was expected to win the starting job when camp started. The Bengals listed him as the starter even though he was missing practices during the holdout.
A few hours before Gresham reached an agreement, Lewis dropped Gresham lower on the depth chart at the position. Veteran Reggie Kelly has returned from a ruptured Achilles tendon in his left leg, but is expected to revert to Gresham's backup again.
"He'll work at it," Lewis said. "We've got a lot of snaps for him to get accustomed and get back in. He'll take 50 percent of the snaps."
Tight end was a major problem last season after Kelly and backup Ben Utecht suffered season-ending injuries during camp. Utecht sustained a major concussion. The Bengals drafted Gresham to give Carson Palmer another over-the-middle target.
The Bengals managed to get their top pick in camp before the first preseason game, a major improvement over last season. Offensive tackle Andre Smith missed the first three preseason games in a holdout, then broke his left foot during practice two days later.
Smith never got up to speed. He appeared in six games and started only one, a disappointment for a team that expected him to take over at right tackle because of his ability to block for running plays. The foot is still bothering him, forcing him to work out separately from the practices so far.