Speaking to the BBC, Mr Hayes said he hoped his apology on behalf of all active republicans will help grieving relatives find "closure".
He said: "My apologies and my heartfelt sympathies to all of you, for the terrible, tragic loss that you've been put through.
Six men were wrongfully convicted for the blasts but no-one has ever been brought to justice.
Mr Hayes, 69, who now lives in south Dublin, said he personally defused a third bomb on Birmingham's Hagley Road after he became aware of the death toll in the first two blasts.
Fears are growing for a heavily pregnant woman who has gone missing in Birmingham.
Carla Morgan, 35, was last seen just before 5pm on Tuesday leaving her home in the Acocks Green area of the city.
He said he had been a member of the IRA for more than 30 years in both Ireland and England and had participated in the group's activities in Birmingham as "an active volunteer".
Until the 7/7 London bombings in 2005, the Birmingham bombings was the worst ever terrorist attack on the British mainland.And all these years you've been trying to find closure.I hope at last God will be merciful and bring you closure. I apologise for all active republicans who had no intention of hurting anybody and sympathise with you." An eight-minute delay before police were warned of the bombs' location led to the death of 21 people and the injury of 182 others, when they exploded in a pair of city centre pubs.Mr Hayes said the bombs had not been intended to kill people.On the evening of the 21 November 1974, a man with an Irish accent called the newspapers to say two bombs were planted in the town centre.