Bury Lawn is the first in the UK to be bought by Global Educational Management Systems (Gems), which plans to open a chain of 200 no-frills schools.
It has been at the centre of a row over poor student morale and an alleged "culture of fear" among staff.
Parents passed a vote of no confidence in the school's management in May after the departure of four heads within a year, and complained after class sizes grew.
Parents said the tipping-point came last month, when Mark Olejnik, deputy head for 15 years, was dismissed and replaced by Dr Sheila Kaye, the school's fifth head.
A Gems spokesman said only 11 out of 495 pupils were leaving the school as a result of the protest.