The Denmark international completed his move to Celtic in a deal believed to be in the region of 2 million pounds ($3.8 million), according to BBC Sport.

"I am delighted to have joined Celtic, one of the biggest clubs in the world," Gravesen told the club's official website.

"When I was made aware of Celtic’s interest, naturally, I was very keen to talk to the club and now having spoken to the Manager, the Chief Executive and other people at the club, I am very excited about this move."

The 30-year-old's first-team chances with Real Madrid became slim after the arrival of midfield duo Brazilian Emerson and Malian international Mahamadou Diarra.

Several Premiership clubs were targeting Gravesen including Newcastle United, Bolton Wanderers, Middlesbrough and his former club Everton but Celtic were the favored destination for him.

Meanwhile, Premiership side Aston Villa completed the signing of Celtic playmaker Stilian Petrov on a four-year contract for an undisclosed fee.

Petrov becomes the first signing for Villa new coach Martin O'Neill.