"Fabio Coentrao officially became Real Madrid's latest signing by signing a six-season contract with the club after passing his medical," Real said in a statement on their website.
Benfica had announced the deal in a statement earlier on Tuesday.
Coentrao, 23, had a contract with the Portuguese club until 2016 and is regarded as one of the most promising left-backs in Europe.
He is the fifth squad reinforcement of the close season for Real's Portuguese coach Jose Mourinho following the acquisitions of Turkey midfielders Nuri Sahin and Hamit Altintop, French defender Raphael Varane and Spanish forward Jose Callejon.
Coentrao joined Benfica from Rio Ave in 2007 as a winger but failed to make an impact in his first season and went on three consecutive loan spells, including a short and unimpressive one at Spanish club Real Zaragoza.
Benfica coach Jorge Jesus recalled Coentrao in 2009 andconverted him into a speedy and tricky left-back who became akey member of the team who won the Portuguese Premier Leaguetitle in 2010 for the first time in five years.
Coentrao's fine club form earned him a place in the national team and he impressed at last year's World Cup.
"The left-back is solid in attack, has excellent dribbling skills, has a powerful shot and is extremely versatile, which allows him to play in any winger position," Real said.
Real spokesman Oscar Ribot could not immediately be reached to comment on Spanish media reports that the club's Argentine defender Ezequiel Garay would be sold to Benfica for 10 million euros and Netherlands midfielder Royston Drenthe would be loaned to the Portuguese club.
