The 23-year-old scored four goals in 62 appearances during his stay with Steaua, as well as earning 19 caps for the Romania national team.
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"We are delighted to announce that we have reached agreement with FC Steaua Bucharest for the transfer of Vlad Chiriches," a statement read on the club's official website.
Chiriches made his international debut in August 2011 and helped Steaua end their seven-year wait for the Romanian league championship last term, and also played part in their succesful Champions League qualifying campaign.
He becomes Spurs' fifth signing of the summer, joining Roberto Soldado, Paulinho, Etienne Capoue and Nacer Chadli at White Hart Lane, while Erik Lamela and Christian Eriksen are set to join from Roma and Ajax.