The departures of William Gallas and Steven Caulker left Tottenham short on numbers at the back, but they have now resolved the problem by signing 23-year-old Chiriches for a fee of around B£8.5million.
Tottenham posted on their Twitter feed: "We're delighted to announce we have reached agreement with FC Steaua Bucharest for the transfer of Vlad Chiriches."
Chiriches played 62 times for Steaua during a two-year period at the club and he has made 19 appearances for his country. The defender is Tottenham's fifth signing of a busy summer which has seen the North London club spend £67million in the market.
"For me, this is something incredible. A dream come true," he said.
Villas-Boas spoke fondly of the centre-back on Thursday night following Spurs' 3-0 win over Dinamo Tbilisi in the Europa League.
"He is an interesting player that has been followed by lots of teams," Villas-Boas said. "He has tremendous qualities coming out with the ball and that's what we like in our defenders. He is a great leader."
Although Tottenham have spent extensively this summer, they are still in the market for new players. Ajax's Christian Eriksen and Roma midfielder Erik Lamela both had medicals yesterday and could complete their respective transfers to White Hart Lane today.
The arrival of the creative duo should be enough to persuade Tottenham to finally allow Gareth Bale to complete his world-record move to Real Madrid.
Chiriches has played at four different Romanian clubs and he also had a one-year spell at Benfica between 2007 and 2008.
The centre-back joined Steaua from Pandurii Targu Jiu, making his debut in July 2011 before helping them to the Romanian Liga I championship last year.