The competitions is being run as part of a wider plan to reorganise the roads at the Old Street interchange, which will see the removal of the "outdated and intimidating" 1960s roundabout.
Organised by Islington Council, in association with the Mayor of London, Transport for London (TfL) and Hackney Council, the contest aims to find an "innovative idea" to rejuvenate the junction, which is next to AHMM's White Collar Factory.
More than 120 registrations of interest were received to reimagine the public realm, with 39 teams longlisted.
A public consultation on the proposals starts today, with a public exhibition displaying all the ideas due to run until 2 March 2018. Following the consultation, a panel will draw up a shortlist of best entries that will be announced later in March.
The planned reworking of the road system will reintroduce a two-way traffic system and see the north-western arm of the roundabout closed to create a peninsular. This will allow the former roundabout site to be converted into an "attractive new pedestrianised public space".
Plans for the highway reorganisation are due to be submitted later this year, with construction due to start in the winter of 2018.
"Old Street is an iconic location, and its transformation will hugely improve the area for pedestrians, public transport users, cyclists and people who live and work nearby", said Islington Council's executive member for environment and transport, councillor Claudia Webbe.
"We have had huge interest in our design open call, and the public exhibition is a chance to have your say on the creation of an exciting, bold, iconic gateway – 39 innovative and inspiring ideas set out in one place, so you can help to shape the future of Old Street."
London's walking and cycling commissioner Will Norman added: "This transformation is going to make Old Street a more pleasant and safer place for all pedestrians and cyclists. It's an area that is renowned for innovation so I'm really looking forward to seeing the range of ideas shortlisted and hearing Londoners' opinions about them."