Wamalwa, 59, was being treated in the Royal Free Hospital in London when he died in the early hours of Saturday, Kibaki said in a statement issued by the Presidential Press Service.
A local independent television station said Wamalwa, who was admitted to the hospital in June, suffered kidney failure.
Friend and comrade
Kibaki said Kenya "had lost a patriot and a gentleman who served his country with dedication to enhance the democratic space." He said he had lost "a friend and comrade".
Wamalwa, a British-educated lawyer, was appointed vice president in January.
His appointment followed the success of the opposition National Rainbow Coalition, lead by Kibaki, against the long-ruling Kenya African National Union party of former president Daniel arap Moi in presidential, parliamentary and local council elections held on December 27.