Work for the £27.3m scheme will include the demolition of the current theatre and construction of a new three storey theatre.
The Everyman will close on 2 July with construction work scheduled to begin two months later.
It is expected to take about two years for the improvements to be carried out.
Government cuts have made arts funding a sore point for most theatre companies, but the Everyman has managed to put together enough money to carry out its ambitious plans.
The venue will be constructed of red brick and will feature a new frontage comprising 105 life-sized portraits of Liverpool people transferred onto cut aluminium shutters.
Interested firms have until 18 May to submit PQQs, with tenders due to be invited in August 2011.
Acuity Management Solutions is advising the trust on the bid process.