The 51-year-old specialist has agreed on a three-year deal with the 33-time La Liga champions who have been without a manager following Zinedine Zidane's resignation on May 31.
Under the Frenchman's management, Real claimed an unprecedented three Champions League titles in a row.
Lopetegui led the Red Fury to the 2018 FIFA World Cup finals without suffering a single defeat in their ten World Cup qualifying matches and recently extended his contract with the Spanish Football Federation until 2020.
READ MORE: Real Madrid Coach Zidane Announces Decision to Leave His Post
Before taking charge of the senior Spanish team, Lopetegui worked with the Spanish youth national teams winning the European Under-19 Championship in 2012 and the Under-21 Championship in 2013.
Spain has been drawn in Group B and will play reigning European champions Portugal in Sochi on June 15, Iran in Kazan on June 20 and Morocco in Kaliningrad on June 25.
