United were known to be in the market for a high-profile striker having lost Wayne Rooney and Zlatan Ibrahimovic - the latter of whom has since rejoined the club - and they eventually brought in Romelu Lukaku in a deal which could rise to £90m.
Chelsea were also thought to be in the running for Lukaku, and Morata admitted that he did not think they were interested in signing him from Real Madrid until manager Antonio Conte convinced him otherwise.
"I had various offers this summer, not only Chelsea and Manchester United but also from different leagues. It was a good situation for me. The most important and best conversation I had was with Conte, he wanted me to come here," he told the Daily Mail.
"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. Last summer it was close. 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."
Morata has scored three goals in his opening four Premier League appearances for Chelsea, who host London rivals Arsenal on Sunday.