The music and drama festival will take place on January 14, Russia's old New Year according to the Julian calendar.
The 3.5m high model is the work of Russia's Ice Sculpture Association, led by Viktor Chernyshov. The group was supplied with 12 tons of ice blocks, and worked at a low-temperature workshop in Kent, near London. The parts were then assembled on Trafalgar Square.
The sculpture was created as part of an exchange program between London and Moscow, under which an ice model of the Parliament Clock Tower of London's Palace of Westminster - commonly known as Big Ben - will be built on Pushkin Square in Moscow.
Due to London's warm winter, the sculpture on Trafalgar is already beginning to melt.
"It is of course sad to see this, but we hope Big Ben in Moscow will last longer," one of the sculptor's creators said.
The program is being carried out with the collaboration of London and Moscow mayors Ken Livingstone and Yuri Luzhkov, and the Russian-British Cultural Association.
