A "remarkable" 35 per cent of pupils in 41 schools got an A pass, compared with the national average of 15.3 per cent, the council says.
More than 8,200 pupils in the independent sector sat Standard grade, Higher and Certificate of Sixth Year Studies examinations this year. Students in secondary 5 on average sat 4.2 subjects and 88 per cent gained A-C awards.
Pupils at Standard grade took an average of 6.8 subjects and 51 per cent gained the highest award. The 900 pupils who sat A-levels as well as Scottish qualifications, or as an alternative, did equally well. Eighty-nine per cent passed at A-D and 28 per cent got an A band.
Judith Sischy, the council's director, said the success was down to "hard work, commitment, enthusiasm and determination".
Mrs Sischy said: "Society puts a high premium on qualifications which motivate young people to work hard. They are keen to do well, to continue their education, to go to university or college and to build a career for themselves. The schools have a positive ethos and feel that it is important for every individual to aim high, whatever their capability."
But she says the results "must be seen in perspective as they are only part of the whole school experience". Academic achievement is enriched by other skills students develop and opportunities outside the classroom.
"Once again the independent schools have produced excellent results, similar to those of previous years, maintaining their high standards and consistent success rates," Mrs Sischy said.
The council represents 31,000 pupils in 75 schools, 4 per cent of the pupil population in Scotland.