The plans include the renovation of the pedestrian tunnel that runs beneath Exhibition Road and proposals for the adjoining area.
The project is led by Kensington and Chelsea council and partnered by Westminster council, the Mayor of London's Architecture and Urbanism Unit, and Transport for London.
Merrick Cockell, the leader of Kensington council, said: "The colleges and museums of South Kensington are world-class. We want a world-class designer to help us showcase the area. The field looks extremely promising."
The scheme is one of 10 pilot projects in an initiative that aims to create or upgrade 100 public spaces in London over the next five years.
London mayor Ken Livingstone said: "I am delighted to support this project to create a high-quality public realm linking these museums and institutions with the Tube station and Hyde Park. I believe it will be a great benefit to Londoners and London visitors."
The design competition will be judged by a panel of assessors including architects Richard Rogers and David Adjaye and the commissioner for Transport for London, Bob Kiley. A shortlist of eight practices will be selected next month to draw up more detailed proposals.