The 29-year-old will link up with former Chelsea manager Jose Mourinho at Real Madrid.
Mourinho brought Essien to Stamford Bridge in 2005 from Lyon.
Essien was also linked with a move to Arsenal on transfer deadline day.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.