"I’m very happy to have the chance to play at this great club," he said on Twitter.
Coentrao signed for Madrid from Benfica in 2011 for 30 million euros (26.33 million pounds).
He will be looking to resurrect a career that has been blighted with injury in his second loan spell away from the Spanish capital following a year at Monaco in 2015/16.
Coentrao has played 106 games in five full seasons for Real, spending the 2015-16 campaign on loan at Monaco. He has never played more than 20 league games in a single season. In that time he has won two La Liga titles, two Champions Leagues and a King's Cup.
He has made 51 appearances for Portugal, although a thigh injury prevented him from taking part in his country's victorious Euro 2016 campaign.
Following an injury-ravaged season at Monaco, where he played 15 league games, Coentrao returned to Madrid last summer.
He made six appearances in all competitions last season but was left out of the squad for the Champions League final victory over Juventus.
(Reporting by Joseph Casinelli; Editing by Hugh Lawson)
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