The move to drop the “golden skirt” policy is a sign of ministers’ commitment to strip red tape from companies to get the economy moving.
Ministers said they were “standing up for British business” and were opposing the plans to impose more “burdensome regulation” on companies.
The European Commission launched a consultation in March proposing forcing companies by law to bring in the quotas.
The suggestion for quotas was praised by Prime Minister David Cameron at a summit in Stockholm in March.
However ministers will say the Government is not going to implement the quotas, and instead will merely encourage firms to hire more women in executive positions.
Figures show that nearly 16 per cent of senior positions are now held by women, up from 12.5 per cent last year. If the momentum continues, the number of women on boards will exceed 25 per cent by 2015.
Theresa May, the Home Secretary and Women’s minister, said: “We are encouraging firms to use women’s talents by helping them see the business benefits. But we must allow them to get on with their job.
“Our voluntary approach is reaping rewards. The past year has seen the biggest ever jump in the number of women on boards, and some of the UK's leading companies are now reporting on gender diversity, which will help more women rise to the top.”