Ipswich Borough Council says it plans to buy part of the former Co-op department store on Carr Street, with the help of Suffolk County Council.
The free school could be run by the Active Learning Trust (ALT), which operates four schools in the town.
Borough council leader David Ellesmere said he was glad "a very complex project" could happen, after previous setbacks.
A proposal for a new free school on the site was rejected by the government in April.
For more stories, visit BBC Local Live: Suffolk
A spokesman for the borough council said the cost of the land was "commercially sensitive" so would not be revealed at this time. The proposed purchase of the site will be discussed by the borough council's executive committee on 19 June.
The Labour-led borough council has agreed to buy part of the store from the East of England Co-op, but will hand most of this land over to the government's Education and Skills Funding Agency (ESFA).
It will retain a small part of the site for use as a car park, with revenue from that used to cover the purchase cost of the store.
The Co-op would retain the remainder of the site to the west of Cox Lane.
The choice of free school provider is the responsibility of the ESFA. The borough council says it is anticipated it will be run by the Active Learning Trust (ALT), which already operates Chantry Academy and Gusford, Sidegate and Hillside primary schools in the town.
Colin Noble, leader of Conservative-run Suffolk County Council, said the move demonstrated the authority's "commitment to addressing the educational needs in our county town".
A new school could open in Ipswich town centre in 2019.