The 23-year-old was heavily linked with a summer move to either Liverpool or Arsenal, after failing to break into the Spanish champions' first team last season. Sahin arrived at the Bernabeu from Bundesliga club Borussia Dortmund in 2011. Given his lack of form and inability to break into the Los Blancos squad, Madrid coach Jose Mourinho earlier sanctioned a loan move to help his player get back on track.
Meanwhile, Reds' boss Brendan Rodgers has heaped praise on Sahin.
"We are delighted to welcome Nuri to Liverpool and also to say thank you to Real Madrid for loaning us such an exciting talent. Nuri Sahin is a player with great technique and motivation and someone who will fit in smoothly to our playing model. We welcome Nuri into the Liverpool family and wish him good luck in his efforts to make us successful in our future," Rodgers said.
Madrid boss Jose Mourinho has already backed Sahin to shine in the Premier League.
No Talk on Dempsey
In other Liverpool transfer news, Rodgers has refused to comment on the controversy surrounding the Anfield club's pursuit of Fulham's American forward Clint Dempsey.
It has, however, been confirmed that the Cottagers have lodged a formal complaint against the Reds after Rodgers announced his interest in the American during a news conference. Liverpool could now face a hefty fine and even a points deduction if found guilty of "tapping up" the player.
"For me there is nothing to say on it. This was something I was aware of a number of weeks ago. That has been dealt with in-house," Rodgers stated.
Dempsey has been once again left out of the Fulham squad due to face Manchester United at Old Trafford, after refusing to play against Norwich City in the season opener. Fulham thrashed the Canaries 5-0.