The visualisation has been released just weeks after the AJ exclusively published sketches of the scheme (AJ 24.3.04).
Working alongside Cecil Balmond from Arup, the Portuguese pair stepped in to rescue the project back in January, after it became clear the original architect MVRDV would be unable to complete its scheme in time (AJ 27.1.05).
As a result, the Dutch practice has been given an extra year to develop its ambitious plans for a 23m-high mountain.
Meanwhile, Siza and Souto de Moura now have the chance to build their first scheme in the UK.
The duo will follow in the footsteps of Oscar Niemeyer, Toyo Ito, Daniel Libeskind and Zaha Hadid, who have all previously designed temporary structures on the site in Kensington Gardens.
The gallery hopes to open the doors to the new pavilion in June.