Kajima built the schools under the Private Finance Initiative and is being paid by local authorities to run them until contracts run out, ranging from 2029 to 2035.
The bank set up the investment company last year - the HSBC Infrastructure Company Limited (HICL) - to invest in such projects.
One of its advisers, who did not want to be named, said the attraction of investing in the schools was that they guaranteed a steady, long-term income. The company was likely to invest in more, she said.
The deal has proved to be controversial with teachers at some schools. At Haverstock Secondary in Camden, London, one of the 16 schools affected, staff were surprised by the alteration in ownership.
Kevin Courtney, NUT secretary for Camden, said: "It is very odd that companies can buy parts of schools from other companies without the school even knowing. It could have a direct effect on a school's reputation. I don't think that HSBC's reputation is damaging, but it could be an issue in other cases."
The other 15 schools affected are: three primary schools and a secondary school in Ealing, west London; three primaries and a secondary in North Tyneside; the Darlington Education Village, which is made up of four schools; and Wooldale Centre for Learning in Northampton, which consists of a nursery school, primary, and secondary. Northamptonshire council said it had been informed of the change, which was within the remit of its contract with Kajima.
HICL has already spent pound;80 million buying stakes in three schools in Wales, three in Scotland, and a sixth form college in Leicestershire which is sponsored by the Ministry of Defence.
The deal is not expected to lead to differences in the ways the schools' facilities operate, as Kajima has agreed to continue to manage them day-to-day, including renting out their premises in the evening to sports teams and other clubs.
The NUT has campaigned locally against Kajima's involve-ment in schools on a range of grounds, including that it has carried out construction projects for Burma's repressive regime.
Kajima revealed in 2005 that it had made an pound;80 million loss on its school projects after problems including delays constructing Haverstock school, which left its pupils being taught in sports halls and community centres for four weeks.
HSBC already plays a significant role in England's state schools. It has given more than 100 schools funding to gain specialist status, and is believed to be the largest employer of school governors.
The HSBC Global Education Trust donated pound;1 million to the Government to pilot a scheme to provide a year's private tuition for looked-after children and has also funded schemes to promote teaching Mandarin and personal finance.