Work will involve complete refitting and refurbishment of one of the school’s 5,000 square metre blocks to transform it into a science and technology centre.
A new full-size sports hall will also be built including a new dance and drama studio.
Bam has lodged a planning application with Bristol City Council with work set to start on site in July and be completed by April 2013.
Headteacher Richard Clutterbuck said: “We have worked closely with the team from Bam over the last few months and I am really excited by the final plan we have agreed.
“Bristol Free School will have superb, state of the art facilities, enabling it to continue to go from strength to strength.”