The London International Festival of Theatre (LIFT), working with the London-based architecture charity, will launch the search for ideas on 8 May.
The 'LIFT New Parliament', a £400,000 transportable meeting and performance space, will be unveiled at the LIFT festival in June, before travelling nationally and internationally.
A shortlist of four design teams will be announced in June and awarded £1,500 to prepare for interview.
The public will be invited to contribute to the selection of the final design by voting online for one of the four shortlisted entries.
A winning team will be announced in July.
The brief can be downloaded from 8 May at www.architecturefoundation.org.uk