The 23-year-old moves to White Hart Lane from Steaua Bucharest, where he made 62 appearances after joining from Pandurii Targu Jiu in January 2011.
Chiriches joins a back-line including the likes of Michael Dawson, Jan Vertonghen and Younes Kaboul after a fee reportedly in the region of £8 million was agreed.
The 19-time Romania international made his debut for his country in a UEFA Euro 2012 qualifier against Luxembourg in September 2011.
He featured for Steaua in their run to the UEFA Europa League last 16 last season, which was ended on English soil by Chelsea.
Tottenham saw an earlier move for Chiriches blocked by Steaua's jailed downer Gigi Becali, but Spurs maintained their interest, having sold academy graduate Steven Caulker to Cardiff City earlier in the window.
The centre-back is Andre Villas-Boas' fifth signing of the season after Paulinho, Nacer Chadli, Roberto Soldado and Etienne Capoue.
However, Spurs missed out on the signing of Willian to Chelsea, while Gareth Bale appears on the brink of a move to Real Madrid.
Tottenham have not disclosed the length of contract that Chiriches has signed.
