The 26-year-old has signed a five-year deal with Diego Simeone's side, and he will join up with the team immediately.
"A hard-working right-back, Arias had tremendous success both individually and collectively last season, as he was named Eredivisie Player of the Season and helped PSV win their 24th Eredivisie title," the club said in a statement.
"He also has lots of experience in European football as he played for Sporting CP before signing for PSV in 2013. In total, he played 173 matches for the Dutch club, scoring 10 goals and giving 21 assists.
"He’s been a Colombia international since 2013 and has participated in important tournaments: World Cup (2014, 2018) and Copa América (2015 and 2016)."
Arias has 45 caps for Colombia, and started all four of their games at the World Cup in Russia.
The arrival of Arias signals the end of Sime Vrsaljko's time in Madrid - the Croatian has been heavily linked with a move away and will join Inter on loan.
31 July 2018