The 27-year-old Spaniard was widely expected to depart to either Juve or Arsenal at the end of last season, with Aston Villa skipper Gareth Barry due to join the Merseysiders.
However, a move for either player failed to materialise, with Alonso going on to have one of his best seasons in a Liverpool shirt, anchoring Benitez's outfit to within a whisker of pipping Manchester United to the Premier League title.
The former Real Sociedad midfielder - who has won 64 caps for Spain - did finally depart in August, joining Karim Benzema, Kaka and Cristiano Ronaldo as part of Real's £200 million summer spending spree.
And he has since admitted that Benitez's willingness to sell him a year ago helped make up his mind that it was time to move on.
"It was a reason, but not the only one," he said in Sport.
"I just needed to start afresh, to be part of a new team and get new impressions. When I first heard about the new Real Madrid project, I knew I wanted to be a part of it."
And Alonso insisted he had no regrets about leaving Liverpool - with whom he reached two Champions League finals - and felt that he left the club in the right way.
"I had five great years in Liverpool but it is only healthy for every footballer to change environment after a period in the same club, so I'm very pleased I came here," he said.
"Maybe some of the fans or people in the club don't agree or don't understand my motivations for leaving.
"But i think I can look myself in the mirror and know that I did everything possible for Liverpool, and I was committed throughout. I left Liverpool in a far better condition than when I came in 2004."
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