Getafe ended a 12-year stint in top flight after a 2-1 defeat at Real Betis, while Rayo Vallecano will also drop down a division despite beating Levante 3-1.
Barcelona scored twice in the first half and then late on courtesy Luis Suarez to beat Granada 3-0 and win the La Liga title.
Action from across Europe’s top football leagues culminated this weekend with champions and relegated teams decided.
Real Madrid’s hopes of beating Real Betis could be boosted by the return from injury of Karim Benzema.
Real Madrid’s new coach Rafa Benitez is under pressure early in his stint with the club as they face Real Betis in their League opener.
Sergio Ramos, 29, will sign his new deal together with Real president Florentino Perez at Bernabeu later on Monday.
La Liga has 38 of the 42 professional clubs in Spain’s top two divisions on board.
Lionel Messi scored 41 goals in 37 La Liga appearances this term.
Lionel Messi scores his 400th goal for Barcelona in hard-fought win over Valencia.
Lionel Messi moved ahead of Cristiano Ronaldo in scoring charts as Barcelona won 2-0 at Eibar to stay top.
Barcelona beat Villarreal 6-2 on aggregate while Athletic Bilbao beat Espanyol 3-1 on aggregate.
Rodriguez’s surgery on a broken bone in his right foot was a success. His return is not clear yet.
James Rodriguez headed the opener before going off injured in Real Madrid’s 2-1 victory over Sevilla.
Raul Garcia converted a 57th minute penalty before Jose Gimenez headed Atletico’s 2nd goal in 76th.
Barcelona lost at Real Sociedad in the league on Sunday. Messi only played the second half of the match.