The 24-year-old striker said the presence of Antonio Conte at Chelsea is what made his decision to move to London rather than Manchester an easy one.
Morata said he was unaware of interest from Chelsea at the beginning of the summer and thought they were going for "a different player".
He does not know whether that player was Romelu Lukaku, who eventually joined Manchester United for £90m.
"I had various offers this summer, not only Chelsea and Manchester United but also from different leagues," he told the Daily Mail. "It was a good situation for me.
"The most important and best conversation I had was with Conte, he wanted me to come here.
"At the start of the summer, I didn't know that Chelsea were interested in me. I thought they were in for a different player, maybe Lukaku or maybe someone else, I don't know. I didn't think the option of Chelsea was open.
"But I spoke with Conte several times - and not only this summer. I felt in debt to him. He signed me for Juventus but left very quickly to manage Italy.
"I always wanted to play for him after that. It was only two months with him but it felt like I'd known him forever. When I knew he wanted me this summer, I didn't think twice. I did everything I could to make the move happen."
The Spanish striker also revealed he was closing to joining Chelsea last summer, after Conte was appointed as manager.
"Last summer it was close," he said. "Cesar Azpilicueta was a bit annoyed because he had already started house-hunting for me.
"We'd even got estate agents on board. This time Cesar has sorted everything.
"When I spoke to Conte last summer, I said 'If I'm going to leave Real Madrid, it will only be for Chelsea'.
"I remember I was with my wife after hearing him out and I said 'Chelsea are going to win the league this season.' And that's exactly what happened. Now we need to repeat it."