Modric has long been linked with a move to Madrid, but the switch was only finally completed on Monday when the Croatia international passed his medical and signed a five-year contract at the Bernabeu in a transfer that will reportedly see the Spanish champions pay Tottenham ?33million.
The signing comes following a less-than-successful start to the season for Jose Mourinho's team, who have taken just one point from their opening two Primera Division games and lost the first leg of the Spanish Supercopa to Barcelona.
Last night's defeat to local rivals Getafe left Madrid five points behind arch-rivals Barca in the standings, but Butragueno has said there is no relation between that and the addition of Modric.
"We would've liked Luka to be here before and it was yesterday when we finally closed the deal. It has nothing to do with the results," said Butragueno, a legendary former striker at Madrid and now the club's director of international relations.
He also told Modric: "We are convinced that with your talent and quality you are going to help us achieve our goals."