Downing Street gave the broadest hint yesterday when the prime minister's official spokesman said that the government had announced the weekend before last that a ruling would be made public in 10 days.
Downing Street said parliament would be the first to hear. Mr Byers faces his regular hour of questions and answers today, an obvious opportunity to make his decision public.
The transport secretary will attach strings to his decision, which will allow Heathrow to increase passenger numbers by a further 20m by 2007 when the project is expected to be completed.
He is likely to put further restrictions on night flying and a limit on the daily movements of aircraft in and out of Britain's largest airport.
Promises made by previous governments on the limit to Heathrow's expansion have usually been set aside. The most recent occurred over the building of terminal 4, where restrictions on passenger numbers and flight movements have been broken.
The terminal will be built by BAA, the airports operator, which has so far spent almost £300m in preliminary work. The most substantial is the construction of an underground road linking Heathrow's central area to a site near terminal 5.
The final cost of the project, which will be the home base for all British Airways' flights, is likely to exceed the £2.5bn forecast. It will be built on the site of an old sewage works on the west side of the airport.
Peter Brown, spokesman for the 11 local authorities which have opposed terminal 5, said: "We shall be looking very closely at the conditions attached. We want the conditions enforced and we do not want a repeat of the terminal 4 situation when promises on the number of flights were broken in a matter of months."
A BAA spokesman said: "We would expect some conditions to be laid down. It's too simple to say promises were broken as far as terminal 4 was concerned. Recommendations were made but circumstances changed."
The government decision follows a public inquiry into T5 which took place between 1995 and 1999 and cost the taxpayer £80m. Roy Vandermeer QC, handed his report to the government at the end of last year. But Labour decided not to announce its approval before the election because it could have had a detrimental impact on 20 constituencies around Heathrow.
T5's backers said that Heathrow needs to meet passenger and airline demands to allow London to maintain its position as an important European business and economic centre.
Its opponents claim that there are other parts of the south-east, particularly Stansted, which could be expanded without causing much damage to the local environment.
Heathrow last year handled more than 62m passengers. BAA says that T5 will be able to cater for up to an extra 30m, allowing the airport to handle 85m passengers. But T5's opponents fear that the annual figure could rise to around 100m.