Consent from Parliament had never been in doubt and was mainly procedure after the General Synod voted in favour of the proposals in July.
The law allowing women to take the top Church job awaits Royal Assent before being presented to the Synod again in November.
Women priests now make up more than a quarter of parish clergy and around half of priests in training.
There are already 23 women archdeacons and six women deans.
The Archbishop of Canterbury, Most Rev Justin Welby, previously said that he hoped the first women bishop could be in place by Christmas.
Speaking at the House of Commons debate, MP Frank Field said: "As well as recognising the consequences of delay, will the Right Honourable Gentleman sound a note of joy, in that the Church will now be able to choose from the other half of the population for its most senior positions, which, all things being equal, must strengthen our hand?"
But Sir Tony Baldry MP, the second church estates commissioner, raised one concern at the debate.
He said: "One consequence of the measure is that it will be possible for women to become Lords Spiritual and to sit in the House of Lords.
"At present, diocesan bishops are appointed to the House of Lords on the basis of seniority, so getting women bishops into the House of Lords could take some time if the normal system of seniority were simply left to take its course.
"However, I am glad to be able to report to the House that there has been consultation with all the main parties on the possibility of introducing a short, simple government bill to accelerate the arrival of the first woman bishop in the House of Lords, and I hope that such a bill will be able to be taken through during this session."