Dutch international Robben spent three seasons at Stamford Bridge

The 23-year-old winger has been linked with the Bernabeu outfit for most of the summer but the fee appeared to be a sticking point between the clubs.

However, Chelsea announced that the transfer had been settled subject to the Dutchman agreeing personal terms on a five-year deal and passing a medical.

The transfer fee is thought to be in the region of �21m.

John Terry said losing Robben was a blow.

"We are very disappointed to lose him," said the Chelsea captain. "He's very young and a world class player.

"He's been a great friend to not only me but all the other Chelsea players. We are sorry to see him go but on behalf of myself and everyone else at Chelsea we wish him well."

The Robben announcement came on a busy day for Real, who agreed a deal for Manchester United's Gabriel Heinze as well as the sale of Cicinho to Roma.

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Robben has been at Chelsea since joining from PSV Eindhoven in 2004, scoring 19 goals in 104 appearances at Stamford Bridge.

However, Real president Ramon Calderon repeatedly expressed an interest in bringing the winger to the Bernabeu.

This summer, Robben was offered a new Chelsea contract but opted instead to push for a move to the Spanish capital.