The Argentina international has moved to the Spanish capital on a three-and-a-half year contract after spending 18 months at Sporting Lisbon
The Argentina international will act as competition for the left-back spot for Filipe Luis, but will be unable to play in the Europa League, having already represented the Portuguese side in the competition.
Insua won the 2007 Fifa Under-20 World Cup with Argentina and had been with Sporting Lisbon since the summer of 2011 making 60 appearances and scoring six times.
Before signing for Sporting, Insua was part of the Liverpool team who finished second in the Premier League in 2008-09.
He started his career at Boca Juniors and also spent time in Turkey with Galatasaray.