The former Chelsea winger put pen-to-paper on a five-year contract with Real on the same day that Gabriel Heinze finalised his switch from Manchester United, the Argentina defender penning a four-year deal with the Spanish champions.

Real have been linked with a move for Robben for over a year, with club president Ramon Calderon pledging to sign the player during his successful election campaign last summer.

No deal was forthcoming then but Real, after months of speculation, finally got their man on Wednesday - much to Robben's delight.

"For me it was really a big relief when yesterday the final word came that I could join Madrid," the 23-year-old said at his unveiling at the Bernabeu.

"I think its a great honour if you're one of the promises of a president. Now I am here I think everybody is happy - the club is happy, I'm very happy."

The Dutchman added: "It has been difficult and it took a very long time. There were many moments when I thought I was going to Madrid the next day, and then it didn't happen.

"But in the end I got here, and although it took very long, I wanted to be here so I'm very happy."

No fee has been confirmed for Robben and Heinze, but reports in the Spanish media suggest the double swoop could cost Real almost $85million in total.

The majority of that outlay is believed to have been on Robben, who Chelsea paid $30million for when they signed him from PSV Eindhoven in 2004.

Robben said of the reported transfer fee: "I know it's a lot of money, I think it shows the interest Madrid had in bringing me here and it gives me a lot confidence.

"They showed over the last few weeks that they were really willing to everything to get me here, and that gave me a great feeling so I am very happy that finally the decision came yesterday."

Robben insists he will remember his time at Stamford Bridge fondly, but admits everything did not go as well as he would have liked.

"I had three very nice years at Chelsea, it was a great experience for me personally," he said.

"I won every prize I could have have won in England, so I'm very satisfied with that. Unfortunately I had too many injuries there so I could not give the impact that I wanted to.

"In my first year I think I had a very good year, but then I had some bad luck and for me I see this as a new start, a new challenge, without any injuries and I hope I can stay out of that terrible (treatment) room for a very long time."

Also being unveiled as a new Real player on Thursday was Heinze, whose switch to the Spanish giants was announced on Wednesday evening, just hours before Robben's move was also confirmed.

Heinze was still considering whether to launch an appeal against the Barclays Premier League decision to block his preferred to Liverpool when Real made their move.

At the Bernabeu, the 29-year-old could well take up the left-back position vacated by Roberto Carlos' move to Turkey this summer.

Roberto Carlos was a virtual fixture in the Real team for over a decade, and Heinze admits the attack-minded Brazilian will be a tough act to follow.

"I think that it is impossible to forget Roberto Carlos. I have come here to give everything. What Roberto Carlos has done is impressive," said Heinze, who does not know if he will be utilised at left-back or in the centre of defence by Real coach Bernd Schuster.

"He (Schuster) will know where I can be most useful," said Heinze. "At Manchester United I always played at left back and for Argentina in the middle, apart from the Copa America."

Lyon were also interested in signing Heinze, who played for Paris St Germain in France before joining United, but the South American insists Real were the club for him.

"It is true that Lyon liked me and I am grateful for that, they are a great club," he said.

"Nevertheless, I preferred Madrid because I think that any player would want to come to this team and for me I could not let this opportunity escape.

"Now at last I am here and I am happy, I could not be more content."

The arrival of Robben and Heinze takes the number of new signings at Real this summer to eight, with Christoph Metzelder, Pepe, Javier Saviola, Jerzy Dudek, Royston Drenthe and Wesley Sneijder already being drafted in.

Real begin the defence of their Primera Liga title on Saturday when Schuster's side host local rivals Atletico Madrid at the Bernabeu.