HMP Oakwood and HMP Birmingham got an overall score of three out of four, meaning they meet the majority of targets, the National Offender Management Service said.
G4S, which manages the jails, said the figures were positive and encouraging.
Earlier reports said HMP Oakwood was failing to tackle drugs and HMP Birmingham faced "significant challenges".
Performance was monitored in areas including public protection, reducing reoffending, resource management and operational effectiveness.
An HM Prison Inspectorate report in February this year said HMP Oakwood continued to have problems with bullying, the use of force by staff and self harm.
The jail near Wolverhampton was heavily criticised after an inspection in 2013, but the February 2015 report also said the jail made "significant improvements" including "a calmer atmosphere" and better staff-inmate relationships.
G4S director for HMP Oakwood John McLaughlin said it had come through "a difficult period" since it opened in 2012 but "the prison, staff and regime have matured".
He said: "We continue to focus on getting more prisoners at Oakwood into meaningful education and training to support their rehabilitation back into communities, help them turn away from crime and ultimately improve public safety."
A report in 2014 found conditions at HMP Birmingham had improved since a private takeover in 2011 and the jail in Winson Green was "making good progress" since G4S took control, but some problems persisted.
The presence of illicit drugs remained "stubbornly high", while some foreign inmates were negative about their experiences, inspectors said.
G4S director for HMP Birmingham Pete Small said: "We continue to work hard with the Ministry of Justice and partners locally including West Midlands Police to improve the prison, play our part in cutting reoffending and ultimately enhance community safety."
Two privately-run jails have scored highly in reports just published.