The source, speaking on condition of anonymity, told ESPN's Chris Mortensen on Saturday that there was no signing bonus, but Williams' salary in 2009 could increase significantly over this year's base of $730,000.
The Miami tailback can increase his 2008 compensation with easily achievable incentives, the source said. Williams, 31, was scheduled to be a free agent in '09.
Dolphins general manager Jeff Ireland said Sunday that the team wanted to keep the 31-year-old running back so "he didn't become a free agent" after this season.
"I wasn't here in the past so I don't really know if he had a lack of dedication in the past," Ireland said. "I mean, I know what I read and I know what circulates in NFL circles.
"But when we sat down coming here, we said, 'We're going to give this guy every benefit of the doubt. And he's got to show us that he is dedicated.' And he's done everything that we've asked him to do. And we feel very good about our decision to extend him."
Williams, the 2002 NFL rushing champion, has played in only 13 games since retiring in the summer of 2004. He has tested positive for marijuana at least four times since the Dolphins acquired him in 2002, and their franchise-record playoff drought began that same year.
In July, the 1998 Heisman Trophy winner said he felt good going into the Dolphins' season.
The Dolphins, coming off a 1-15 season, are hoping that Williams can return to his star form -- and fulfill his contract.
"You guys see it out there, we see it out there," Ireland said. "He's done an excellent job in the weight room, the meeting room, he's come out there and he's jumped out at us on tape. He looks good in the preseason. So everything we've seen since we got here ... he's done everything we've asked him to do."
For now, Williams is showing the kind of effort that once led the NFL in rushing and won him the Heisman Trophy in college at Texas.
He didn't miss a voluntary practice in Miami's strict offseason workout program under the new Bill Parcells-led regime. And he has bulked up to about 230 pounds, the weight he played at in his prime.
Williams has said this season is partly about changing his legacy.
"The way I left made it difficult," Williams said during training camp. "To come back and clear my name is important to me."
A cell phone message seeking comment from Williams' agent, Leigh Steinberg, was not immediately returned.
Williams' comeback in 2007 lasted less than one half. He gained only 15 yards on six carries before he fumbled, was stepped on and tore his chest muscle against Pittsburgh.
This year, Williams is teamed with Ronnie Brown, who was on pace for a career season in 2007 before he tore a ligament in his right knee. Both running backs' contracts expire at the end of the 2009-10 season.
Ireland said the Dolphins wanted to make sure Williams remained signed with Brown.
"He's a player that's shown he can play," Ireland said. "He's shown us that he can play. So we didn't want him to make the free-agent market."
Williams was the only major roster move on a slow day for the new regime of Ireland, Parcells and coach Tony Sparano.
The team claimed New Orleans center Andy Alleman, New York Jets tackle Nate Garner and New York Giants receiver Brandon London off waivers. The team waived receiver Anthony Armstrong, offensive lineman Trey Darilek and linebacker Rob Ninkovich to clear space on the 53-man roster.
Information from ESPN NFL reporter Chris Mortensen and The Associated Press was used in this report.