Miller Construction, part of the Miller Group, has been selected as the preferred bidder for a £235m Building Schools for the Future contract in Leicester.
Work on phase one of the programme, which is due to start next year, will tackle four schools.
The remaining 11 schools will be delivered in three phases over the next six years.
The announcements mean that £1.2bn has already been spent by the government on the BSF programme at preferred bidder stage or further.
So far, nine councils have announced preferred bidders. These include Bristol, Bradford, Newcastle, Greenwich, Sheffield, Leicester, Solihull, Lancashire and Manchester.
The government plans to spend £45bn over 15 years to rebuild every secondary school in the country.