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Real Madrid have signed Real Sociedad midfielder Asier Illarramendi after agreeing to meet his buyout clause of around 39m euros (£34m).

The Spain Under-21 international, 23, signed a six-year contract at the Bernabeu after passing a medical.

"I came to the conclusion that it was an offer I couldn't refuse. It's a unique opportunity," Illarramendi said.

"It hasn't been an easy decision; it has been very difficult for me because Real Sociedad have given me so much."

Illarramendi came through the youth ranks at Sociedad, and helped the club finish fourth in La Liga last season to secure a place in the Champions League.

He then played every game as Spain Under-21s won the European Under-21 Championship in Israel earlier this summer.

Illarramendi is Real Madrid coach Carlo Ancelotti's fourth signing of the summer after Isco joined from Malaga for £23m, Dani Carvajal moved from Bayer Leverkusen and Casemiro's loan deal from Sao Paulo was made permanent.

Sociedad president Jokin Aperribay was reluctant to sell Illarramendi.

He said: "We have a very important year ahead of us with a young coach (Jagoba Arrasate) and we wanted all our players to stay.

"We told Real Madrid that we wouldn't negotiate, and we said the same thing to Asier and his agents. We fought very hard for him to stay and it's been a difficult few days because we really wanted him to stay."