"We're delighted to announce we have reached agreement with FC Steaua Bucharest for the transfer of Vlad Chiriches," Spurs announced on Twitter.
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 £67m in the market.
"For me, this is something incredible. A dream come true," he said.
Chiriches will compete with Jan Vertonghen, Younes Kaboul and captain Michael Dawson for a place in the heart of the Spurs defence. Villas-Boas spoke fondly of the centre-back on Thursday night following Spurs' 3-0 win over Dinamo Tbilisi in the UEFA 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."