The number of Oxford and Cambridge graduates teaching in state schools has nearly doubled to 11,000 in the past 12 years, a report says.
The Sutton Trust education charity report says education is the top area of employment for Oxford graduates.
Teach First, which recruits top graduates into teaching, said the profession's status had been raised.
Independent schools are three times more likely to have Oxbridge-educated teachers than state schools,
The report says: "While there remains a gap between the state and independent sectors, however, there is evidence that this gap has narrowed.
"Since 2003, and extrapolating from the findings of this report, it can be estimated that the state sector has recruited about 6,000 additional secondary teachers from Oxbridge, while recruitment to the independent sector from the same has remained broadly stable.
"Extrapolating these figures for the nation as a whole, it can be said that there are now more Oxbridge-educated graduates in the state sector, than in the independent.
"This suggests that, while there is clearly a long way still to go, there has been progress in realising the goals of consecutive governments to recruit more teachers educated at the nation's best universities into the state school system."
Teach First founder Brett Wigdortz said: "Teach First is proud to have played a part in raising the status of the profession, with teaching now being seen as one of the most prestigious careers for the graduates.
"Great teaching and leadership are among the most powerful forces for social change."
The Sutton Trust stresses a top university degree is not the only factor needed for good teaching, but highlights its own earlier research saying solid subject knowledge is a key quality for able teachers.
It also looks at the subject specialisms held by teachers in the state and independent sectors, and cites Department for Education figures saying 86% of state secondary English, maths and science teachers hold a relevant post-A Level qualification.
Teachers of science and maths in independent schools, however, are slightly more likely to have relevant post-A Level than their state counterparts.
Sir Peter Lampl, chairman of the Sutton Trust, said: "Although today's figures show that there has been progress over the past few years, with better qualified teachers and more from Oxbridge, it's vital that we do more to ensure that pupils from low- and middle-income backgrounds are just as likely to access the best teachers as their more advantaged peers."
Nansi Ellis, assistant general secretary at the Association of Teachers and Lecturers, said the change said more about the state of the economy than the status of the profession.
She added: "Being an Oxbridge graduate may well give you some good subject knowledge, but it's not the only place for getting a good degree.
"If you are somebody who has gone through the education system without much struggle, that might mean you are less able to explain things well to children who are struggling."
A Department for Education spokesman said: "This report proves that teaching remains a hugely popular career - there are now more teachers in England's classrooms than ever before, with record levels of top graduates continuing to join the profession.
"We want to ensure that teaching remains an attractive choice for graduates. Our teacher recruitment campaign, Your future Their future, is playing a key role and we continue to offer bursaries worth up to £25,000 as well as prestigious scholarships."