The firing of Dungy comes just two days after the Buccaneers suffered an embarrassing 31-9 loss to the Philadelphia Eagles in the NFC wild card round.
Reports surfaced one day before the Bucs' latest playoff failure that Dungy would be fired if Tampa Bay lost to Philadelphia, and that owner Malcolm Glazer had a tentative agreement with Parcells to become the club's new coach.
According to reports, the hiring of Parcells will be delayed for four-to-six days while he finalizes contract details and begins the process of assembling a staff.
The Tampa Tribune reported Monday, Parcells' deal is believed to be for three years and may include an option for two years or more that would allow him to assume a higher role in the organization should he desire it.
Tampa Bay general manager Rick McKay, who also could lose his job in a Parcells-led structure, met with the Glazer family on Sunday in an attempt to save Dungy's job.
Dungy, 46, led the Bucs from football obscurity to being a contender and is the only winning coach in a mostly dismal history of the franchise.
"It's been a privilege to work with not only Tony Dungy the coach, but Tony Dungy the man," Glazer said. "This has been a most difficult decision. Tony has done great things for our football team and our community. I know I speak for the whole Tampa Bay community and all the Buccaneers fans in wishing Tony and his family the best."
In six seasons as coach, Dungy posted a 56-46 record and led the Bucs to the playoffs four times. The high point during the Dungy era came in the 1999 season, when the Bucs advanced to the NFC championship game before losing to the eventual Super Bowl champion St. Louis Rams.
Tampa Bay went 2-4 in playoff games under Dungy and has failed to score a touchdown in its last three postseason contests.
The 60-year-old Parcells is no stranger to postseason success, coaching the New York Giants to two Super Bowl titles in 1986 and 1990 while also guiding the New England Patriots to a trip to the Super Bowl following the 1996 season. He announced his retirement as coach of the New York Jets in 1999 and resigned as director of football operations last season.
Glazer has had an infatuation with Parcells since rumors surfaced at last season's Super Bowl that Glazer was pursuing him. However, Glazer decided to stick with Dungy for another season, although he refused to give him a contract extension, and the Bucs qualified as the final NFC wild card with a 9-7 record.
Many Tampa Bay veterans said as far back as last season's playoff loss at Philadelphia that the roster should be dismantled should the club not progress to Super Bowl XXXVI this season.