Reding made the decision yesterday but stated on Twitter: "Europe has a lot to gain from more diverse corporate boards."
She added: "The European Parliament has called for action to get more women into boardrooms. The time to act is now."
Businesswoman and Dragons' Den star, Hilary Devey told HR magazine she was pleased with the decision: "As you know, I do not think quotas are the answer. Self regulation is the best answer not imposition."
Helen Wells, director of Opportunity Now the gender campaign from business in the community, said: "If the vote is passed, we will be left with a quota that masks the symptoms of gender equality in the workplace, but does not address the root causes."
Wells added: "All of these legislative changes are designed to support gender equality in the UK's workforces, and are a strong indication that this issue is seen as vital to the country's economy."
Conservative MEP for London Marina Yannakoudakis, who wanted the plan scrapped, said: "It is clear that quotas imposed by the EU are unwanted and unworkable.
"I hope Ms Reding will take the hint: member states don't want quotas, the commission doesn't want quotas and I know many members of the European Parliament don't want quotas.
"Let's put a stop to this quota nonsense once and for all and talk about the real issue of supporting diversity in business."
However Socialist Group leader Hannes Swoboda of Austria said Reding should carry on pressing to get the quota system into EU law: "It would be very sad and regrettable if the commission were unable to present a strong proposal on promoting gender balance in the senior management of companies because of pressure from business and prejudice."
European parliament political group, The Greens European Free Alliance, show their support for the quota in the video below.
Gender quotas have already been introduced in domestic law in France, Italy, Spain, Iceland and Belgium. Norway, which is not an EU member, has had a 40% minimum boardroom requirement for women for a decade.
The commission says the share of company board posts held by women in EU countries averages less than 15%, compared with 16% in the UK.
Last month, nine countries, including the UK, wrote to the European Commission calling for the idea of compulsory quotas to be dropped.