Alonso has signed a three-year deal at the Reebok Stadium after turning down the chance to join Portuguese giants Benfica.
Coyle rates the 19-year-old, who can also play left midfield, as a highly exciting prospect having come through the youth ranks at the Bernabeu.
Coyle said: "What I loved about him as well was he could have sat on the bench at Madrid all year and then be pushing on.
"But he wants to come and establish himself as a first-team player in the best league in the world. He has that drive and enthusiasm and no end of talent.
"The whole thing was pleasurable at every moment. His agents, his family were as good as their word.
"When a club with the stature of Benfica comes along it's obviously going to turn your head.
"But all throughout they gave me the commitment Marcos wanted to come to Bolton.
"It's a terrific piece of business to pull this off. Marcos is 19 and has already been involved at a very high level."
Alonso made just one first-team appearance at Real as a late substitute in a 2-0 victory over Racing Santander in April.
He has rich footballing pedigree, with his grandfather having played for Real in the late 1950s and early 60s and his father having spent five years with Barcelona in the 1980s.
He becomes Bolton's third signing for the new Barclays Premier League campaign after the arrivals of Martin Petrov and Robbie Blake.
Alonso said: "It was difficult to leave Real because they are one of the best clubs in the world.
"But I think it is difficult to play at the top in Real.
"To come to Bolton is a very good move. Maybe I could have stayed and played with the first team, but I don't know.
"It's very difficult. But here at Bolton, if I work very hard, I have the possibility to play in the first team."
Coyle admitted the deal was not straightforward but is confident the club will be rewarded for their determination to secure it.
"With a club the size of Real Madrid, there will be complex negotiations," said Coyle, who guided Bolton to 14th last season after quitting Burnley in January.
"It was lengthy because he is a fantastically talented young player.
"As lengthy as it was to bring him here, it was certainly worthwhile."
Alonso is not match-fit after an ankle injury and Coyle will not rush him, but the player is confident of being ready for the start of the season next month.
"I will start training on Thursday and I think I will be perfect for the first league match," he said.