The offer, which is worth pounds 50m more than BSkyB had originally bid, values each Manchester United share at more than 241p.
Details of the offer are expected to be announced to the Stock Exchange this morning. The news is likely to send Manchester United shares, which slipped 6.5p to 200p yesterday, soaring again.
The deal crowns more than four months of talks between the two sides, culminating in two days of almost continuous negotiations.
Directors of BSkyB and Manchester United spent most of yesterday locked in discussions at the City offices of HSBC, the investment bank that is advising Manchester United. BSkyB is initially thought to have insisted that pounds 575m was its final offer. But Manchester United's board - led by its chief executive, Martin Edwards, and chairman, Professor Sir Roland Smith - held out for a higher sum. Eventually BSkyB, which is keen to close the deal as soon as possible, raised its bid.
Mr Edwards, who is the club's largest shareholder with a 14 per cent stake, is likely to accept BSkyB's offer, making it harder for a rival bidder to get involved.
However, the takeover is not a foregone conclusion. The Government is likely to come under intense pressure to ask the Monopolies and Mergers Commission to examine the bid. If it does so, the commission could recommend the deal be blocked, although most observers believe there are no competition grounds to prevent it.
The deal also requires the approval of Manchester United's shareholders, many of whom are supporters of the club. A group of shareholders has come together to oppose the bid. Called Shareholders United Against Murdoch, the group has pledged to write to the 15,000 individual shareholders, who control 23 per cent of the club. The anti- Murdoch group has been set up by the author Michael Crick, a media consultant, Richard Lander, and two advertising executives, Richard Hytner and Ben Langdon.
Other bidders could also enter the fray. English National Investment Company (Enic), the financial group that owns 25 per cent of Glasgow Rangers and holds minority stakes in a number of continental European clubs, is at present deciding whether to mount a counter-bid. It emerged yesterday that Enic is poised to announce in the next few weeks that it has taken control of two more European clubs - Bordeaux and a Swiss club, thought to be Sion, the team that supplies most of the national side.
But Enic would have to rely heavily on its financial backers to afford a bid for Manchester United.
Industry analysts yesterday played down suggestions that another bidder could be found. Television groups such as Carlton Communications, Granada and United News & Media are now thought unlikely to take on BSkyB.
The analysts pointed out that Manchester United would not be worth as much to another buyer as it is to BSkyB, which already holds the rights to broadcast Premiership matches. What's more, other football clubs such as Leeds United, Tottenham Hotspur and Aston Villa could be bought for a fraction of the price that BSkyB is willing to pay for Manchester United.