This is an increase of 3% on last year.
This year there were 5,895 applications for places compared to 5,813 the previous year.
A small number of pupils were not allocated a preferred school and the county council’s Admissions and Transport team are working closely with the families affected by this.
The news comes on the same day that according to the council some national papers incorrectly reported a 1,983 school place shortfall in the county.
The council’s cabinet member for education and skills Cllr Zahir Mohammed said he was very concerned about the publication of incorrect data.
He said: “These figures result from a misinterpretation of data provided to an FOI request.
“We have in excess of 6000 secondary school places available in the county this year and fewer than 5900 residents seeking a place.
“We actually accommodated over 790 non-Buckinghamshire children whilst 563 Buckinghamshire children successfully applied for schools outside Buckinghamshire.
“As decisions from parents are received, any places that are refused will be re-offered to children on the waiting lists in later allocation rounds.
“Applications from out of county hopefuls did increase by about 570, such is the attraction of a Buckinghamshire education.
“We had to refuse 1361 out-area applications in the first round but would hope over time that more can be offered.
“However we would of course expect their own borough or county council to find a place for those children if this does not happen.”
Mr Mohammed added: “Overall, this is fantastic news.
“Not only has the first choice school preference offers increased, but crucially we also have the places available for all our own children.”