The nurseries, in Teddington, Epsom, Morden and two in Sutton, were previously run by Petits Enfants and acquired by Leapfrog in 2004.
Bright New Minds is run by business partners Ian Morgan and Nicola Smith, who joined forces to buy their first nursery in Woodley, Reading, last October. The Leapfrog acquisition means Bright New Minds now has seven nurseries and 390 childcare places.
Bright New Minds' new head office will be at the Teddington site. The nursery was highlighted for flouting hygiene rules in the 2004 BBC-TV investigation 'Nurseries Undercover'. Mr Morgan said it had undergone several complete changes of staff and management since then.
He added, 'The current manager has worked tirelessly to achieve a major step forward, with a satisfactory Ofsted inspection last year. We have a great set of highly committed managers who have been very supportive. '
Leapfrog, now with 88 nurseries, said that the decision to sell the sites was based on a review 'to determine which locations and type of nursery best meets the needs of the Leapfrog parents and children, while achieving acceptable returns on investment'.
Nord Anglia Education, which owns Leapfrog, said in its AGM statement that there had been 'a slight improvement in nursery occupancy during the course of this year'.
In January, occupancy was at 55.4 per cent - 2.5 per cent less than last year.
Leapfrog's chief executive Andrew Fitzmaurice said, 'It's low at the moment because it's just after Christmas. We're taking steps to improve occupancy.'
The nursery division made a profit last year when occupancy was on average 60 per cent, he added.