Edwards, the No. 3 overall pick, is expected to sign his contract on Thursday and practice with the Browns for the first time, ESPN.com's John Clayton has confirmed.
With incentives, Edwards could potentially make as much as $40 million under this contract, according to Clayton.
Edwards' camp originally disagreed with the Browns' because the team wanted him to sign away some of his rights to marketing money, Clayton reported.
The team wanted Edwards to give the Browns first right of refusal on the marketing of his name and image, according to Clayton. Leigh Steinberg, agent for 2004 Steelers first-round pick Ben Roethlisberger, said Wednesday on ESPN2 that his client earned $4.5 million in sponsorship money during his first year in the league.
It appeared Edwards would sign his deal hours earlier after arriving at the team's headquarters, but things took a strange turn as he and Smith bolted after negotiations hit a snag.
The pair, along with Edwards' parents and other family members, drove away in a three-car caravan without finishing the deal.
"You don't have a deal until you have a deal," Smith, sitting
in the passenger seat of an SUV driven by Edwards' father, Stan,
said at about 6:30 p.m. "We're leaving Cleveland."
They didn't get far as Smith stayed in touch with the club and was able to complete a contract that could pay Edwards nearly $20 million in guaranteed money.
Smith and the Browns had exchanged as many as seven proposals while struggling to find common ground. The sides have been hung up on, among other things, the contract's length, maximum value and guaranteed money.
In the past few days, they've been discussing a five-year package -- a concession to a request by Smith.
Following practice, Browns coach Romeo Crennel was aware that Edwards and his agent were in the building. And like everyone else, Crennel figured a signing was imminent.
"To my knowledge, no contract has been signed," Crennel said. "Maybe they're still working that out."
Once he signs, Edwards, who was supposed to report on July 25 with the club's other rookies, will be required to pass a conditioning test of several 300-yard shuttle runs.
"He should be able to run it right now," Crennel said. "If he
can't, he hasn't been working out enough."
Crennel was asked what his first words for Edwards will be.
"I'll tell him, 'Go run,"' Crennel said.
While he's been absent, the Browns have installed a big chunk of the offense they'll use this season. Edwards is even further behind after missing the club's minicamp in June because of a family funeral and injury.
Crennel is confident Edwards will eventually catch up.
"He's going to get acclimated," he said. "It's just going to take a little time, but it's going to happen. It could very well take him a full year because he has missed this much camp. He's going to learn. The guy is going to be a good player, but it's going to take time.
"It's not going to happen tomorrow."
The Browns open their exhibition season Saturday night at home against the New York Giants, but Crennel said he would wait to see
what kind of shape Edwards was in before deciding if he'll play.
As for Edwards' two-week holdout, Crennel said it wasn't a distraction.
"If I didn't have any receivers who I thought could play, maybe
then it would be a distraction. But I've got some guys who can
play," he said. "That's football. This is the NFL. Guys hold out.
Guys walk out. And you have to deal with it."
Edwards, who nearly jumped to the NFL following his junior season, finished with 252 career receptions, 3,542 yards and 39 TDs with the Wolverines. Last season, he won the Biletnikoff Award as the nation's top wideout and was the Big Ten's offensive player of the year.
Information from ESPN.com senior writer John Clayton and The Associated Press was used in this report.