Tottenham have reportedly paid £8.5 million for Chiriches, who made his international debut for Romania in August 2011.
In a statement on their website, Spurs said they were “delighted” to welcome Chiriches to White Hart Lane.
The 23 year old helped Steaua win their first Romanian League title in seven years last season and has also made 19 appearances for the Romanian national team.
Chiriches made 62 appearances for Steaua and will strengthen Tottenham boss Andre Villas-Boas defensive options following the departures of William Gallas and Steven Caulker from White Hart Lane earlier in the transfer window.
The Romanian’s move to Tottenham could trigger Gareth Bale’s transfer to Real Madrid after the Welshman failed to show up at training with his Spurs team-mates for the third consecutive day.
Bale is angry that his move to Real Madrid is taking so long but Spurs are determined to sign several players before the Welshman will be allowed to move to the Santiago Bernabeu.
However, Bale seems set to move to Real Madrid before the transfer window closes and could become the most expensive player in football history.