Although the plea is not an admission of guilt, Tyson awaits sentencing early next knowing that he could be given up to 10 years on each count.
"He admits to losing his temper on the side of the road," Tyson's lawyer, Paul Kemp, said.
Tyson told the judge in the court in Rockville that in deciding his plea he was not promised leniency and does not expect preferential treatment in sentencing. He also said he was aware his plea could affect his probation for a 1992 rape conviction in Indiana.
"The state was prepared to present the facts in the case," said the assistant State's Attorney, Carol Crawford, who objected to the judge's acceptance of the plea.
The charges stem from an accident on 31 August involving his wife, Monica, in Montgomery County, in suburban Washington, DC.
Abmielec Saucedo and Richard Hardick said that Tyson, in an outburst of road rage, kicked and punched them following the accident. They have reached an out-of-court settlement with Tyson to avoid a civil suit in the case.
"The complainants will testify at sentencing that this is the appropriate plea," Kemp said.
Outside court, Tyson would not discuss the incident, but he did talk about the fight he has lined up against Francois Botha, a South African, on 16 January. The Nevada Athletic Commission returned Tyson's boxing licence in October, having revoked it after he bit off part of the world champion Evander Holyfield's ear during a heavyweight title fight in June 1997.
Holyfield is due to take on Britain's World Boxing Council champion, Lennox Lewis, at Madison Square Garden in March, and the winner will then fight another Briton, Henry Akinwande, according to the promoter Don King.
Akinwande, the former World Boxing Organisation heavyweight champion, who has a record of 33 wins, one defeat and one draw, suffered his only defeat last year against Lewis when he was disqualified for failing to fight. He was to have faced Holyfield last June, but the fight was cancelled when Akinwande tested positive for hepatitis.
In a court in Upper Marlboro, Maryland, on Monday, Riddick Bowe, another former heavyweight champion, who is awaiting a probable jail sentence for kidnapping his estranged wife and five children in June, has had an earlier assault charge involving his wife set aside.
A judge shelved the second-degree assault charge from August 1997 on the conditions that Bowe have no violent conduct with his wife and that he complete a 10-day psychiatric evaluation - similar to the one Tyson underwent in order to regain his boxing licence - and any accompanying treatments.
The state withheld the right to reactivate the case at any time in the next 12 months.Reuse content