Owner Andy Lonsdale had promised to invest £1m in the club, which was expelled from the Football Conference in June after failing to pay creditors.
But he was late to court and the judge was not satisfied there were sufficient funds.
West Mercia Police has said officers had been deployed to the Edgar Street ground following "reports of antisocial behaviour involving 20 to 30 people".
The club's debt to their football creditors, including members of the current squad, other club staff and clubs from whom the Bulls loaned players during the 2013-14 season, added up to £148,000.
The MP for Hereford and South Herefordshire has called the move "a victory".
Jesse Norman told BBC Hereford and Worcester it was "a bittersweet moment, but the fact of the matter is that after months and months of delay we have now won though".
"I think think it is the best Christmas present we could ever have wanted and this is the beginning of something very significant and good and long-term and new in football for Herefordshire.
It was the tenth time Mr Lonsdale had been ordered to appear at the High Court in London.
His barristers told the judge the money was definitely in the bank but they had no documentation to prove it.
Mr Lonsdale, who claimed he had evidence of sufficient funds, said he was stuck in traffic and could not get to the court in time, which the judge said "was not good enough".
The winding-up order was issued moments after Mr Lonsdale was due at court, at just after 16:30 GMT.
Supporters have gathered at the club's ground at Edgar Street, where one man said: "We will come back. It may take 10 years, but we'll be back."
Herefordshire Council said: "As Hereford United Football Club (1939) Limited is in the process of being wound up and a liquidator will be appointed, this action triggers the council's right as landlord to forfeit the leases.
"The council will now pursue this and seek to gain formal repossession of all three sites leased to the club.
"Once the ground has been secured, the council will consider the appropriate process for procuring a new tenant to ensure the continuation of football."
It is a sorry state of affairs for a club with a famous FA Cup pedigree and who were flying high in the Football League only 5 seasons ago.