International Airlines Group (IAG), which also owns Spanish Carrier Iberia, has bought the airline from German carrier Lufthansa in a deal which has infuriated rivals such as Sir Richard Branson's Virgin Atlantic.
IAG would own more than half of the landing slots at the UK's busiest airport if the deal is completed.
Virgin, which said it had also made a bid for BMI, said: "British Airways' hold over Heathrow is already too dominant and we are very concerned - as the competition authorities should also be - that BA's purchase of BMI would be disastrous for consumer choice and competition."
IAG said the deal is still subject to a binding purchase agreement and regulatory clearance but it envisages a deal could be signed in the first quarter of 2012.
The proposed deal came as IAG forecast it would double operating profits this year despite reporting a 34% fall in the third quarter to 351 million euro (£305 million).
Chief executive Willie Walsh said acquiring BMI would be good for IAG and the British economy but admitted the group did not have an exclusive deal with Lufthansa and also had yet to complete required accounting checks on BMI.
He did not see any regulatory issues arising, even though IAG would control 53% of takeover and landing slots at Heathrow if it completes the deal.
That percentage was still lower than its rival competitors in Europe at their key airports, he claimed, adding that Lufthansa would not have progressed discussions if it was not confident a takeover would be allowed.
He said IAG would use BMI to expand its long-haul network, especially into the fast-growing economies of Asia and Latin America.
© 2011 Press Association