The teams also swapped their fourth-round selections in 2002 as part of the deal.
The Saints surrendered all of their draft picks in 1999 and a first-rounder in 2000 to Washington for the right to select the Heisman Trophy winner from Texas with the fifth overall pick. That deal was orchestrated by former Saints coach Mike Ditka, who was fired after the 1999 season.
The Dolphins just had to part with the 25th overall pick in the 2002 draft and a third-rounder in 2003 that can turn into another first-rounder, contingent on Williams' performance this season.
After missing eight games due to injuries in his first two seasons, Williams rushed for a career-high 1,245 yards in 2001 and caught 60 passes for 511 yards. But he is considered somewhat of an eccentric and was arrested last month for driving 126 miles per hour.
That did not stop the Dolphins, who ranked 23rd in the league in rushing, from making an offer to New Orleans for the 24-year-old Williams.
"We never like to trade good football players, but this was a deal that we felt like we couldn't pass up," Saints General Manager Randy Mueller said. "It is a trade that works well for both clubs, which is the primary reason why the deal was done. The extra draft picks allow us to concentrate on some of the other areas of our team that need to be addressed."
The presence of running back Deuce McCallister, a first-round pick in 2001 who averaged 5.7 yards per carry in limited work, also made Williams expendable.
"We didn't make this move without considering every angle," Saints coach Jim Haslett said. "We have spots on our roster that we are trying to improve, and we have a good, young player in McAllister who needs to be on the field."
Williams immediately becomes the feature back for Miami, which will not re-sign free agent Lamar Smith, who averaged less than three yards per carry last season after a breakout 2000 campaign.
Despite missing the last six games of the 2000 season with a broken ankle, Williams rushed for 1,000 yards and had 44 receptions. He followed up with his first injury-free season and ranked fifth in the NFC in rushing.
Williams has started 38 of 48 games in his career, rushing for 3,129 yards and 16 touchdowns and caught 132 passes for 1,092 yards.
Overall in his four-year career at Texas, Williams rushed for 6,279 yards, making him the NCAA I-A all-time leading rusher before he was passed by Ron Dayne in 1999.