Joining the two firms are Allford Hall Monaghan Morris; Broadway Malyan; KCAP with Maccreanor Lavington; and schmidt hammer lassen with East Architects.
Barking Riverside is a joint venture by English Partnerships and developer Bellway, and will see the UK's biggest brownfield site be completely redeveloped.
The developers hope the 140ha scheme will provide homes for 26,000 people and include two new primary schools and one new secondary school, while employing 1,500 people.
The project will also comprise 2km of open access to the Thames riverfront, as well as new parkland and shopping centres, over the next 20 to 25 years.
The two winners will be announced by the end of July.