A civilian was also killed at the time.
It had previously been believed that the SAS had fired first.
The shootings at Loughgall RUC station were among the most controversial of the Troubles.
Eight members of the IRA's so-called 'East Tyrone brigade' were shot dead by the SAS in a fierce gun battle at Loughgall on 8 May 1987.
They were killed as they approached the station with a 200lb bomb, its fuse lit, in the bucket of a hijacked digger.
The IRA men who died were the East Tyrone IRA 'Commander' Patrick Kelly, 32; Declan Arthurs, 21; Seamus Donnelly, 19; Michael Gormley, 25; Eugene Kelly, 25; James Lynagh, 31, Patrick McKearney, 32 and Gerard O'Callaghan, 29.
A civilian, Anthony Hughes, 36, was killed and his brother badly wounded when they were caught up in the crossfire.
Previously it was reported that the soldiers fired more than 600 bullets with the IRA men firing 70 shots.
According to the Belfast Telegraph, the Historical Enquiries Team has found that members of the IRA unit opened fire as they approached the police station.
Investigators are believed to have concluded that the IRA members could not have been arrested safely.
It is understood the full findings of the report are due to be released within weeks.
In 2001, the European Court of Human Rights ruled that the British government should pay £10,000 compensation to each of the families of the IRA members killed in the Loughgall incident.