The commission will take over care and welfare school inspections carried out by HMI. Education authorities and independent schools will have to pay for the first time, which will affect both residential provision and early years education.
Ms Jamieson said during a visit to Hamiltonhill Family Centre in Glasgow on Monday that she wanted to see a "robust system of regulation and inspection".
Boarding pupils will have the right to expect "an educationally-rich environment". Help with homework must be available, including "readily available" library and computer resources.
Judith Sischy, director of the Scottish Council for Independent Schools, said independent schools remain concerned about the costs and fear the new arrangements may not be as thorough because the commission will have its hands full.