Morata has already scored seven goals for the Blues since joining for a club-record £58million from Real Madrid in July.
The 24-year-old is the main striker at a club for the first time in his career having been a fringe player at Real Madrid and rotated during his two-year vigil at Juventus.
Antonio Conte played a major part in him joining Juventus in 2014 and then the switch to Chelsea two months ago.
Morata said: “I came to Chelsea because one club and one coach believed in me. Now I have all of these things and I’m very happy.
“Was it a big move for me to become the first-choice striker? It’s the most important thing.
“It’s (moving to England) always a difficult challenge. It’s the most competitive league in the world. Yes, it’s physical. And it’s the league with the most teams who can win the title.
“There are strong teams, but we’re very happy because we’re fighting for the Premier League too.”
Morata was subject to a lot of intense scrutiny on joining Chelsea, especially as he was replacing Diego Costa up front.
Things didn’t start too well as he missed a penalty during the shoot-out defeat to Arsenal in the Community Shield.
He added: “My start? It’s not real. In the first official match I made a mistake and I suffer for a few days.
“The people don’t see the situation, but I grew up, take out my character and now the things are okay and we hope to continue like this.”
Morata scored his first Champions League goal for Chelsea in the impressive 2-1 win at Atletico Madrid on Wednesday night.
They now face a tough task in the Premier League as they face title rivals Manchester City on Saturday.
Morata said: “It’s another big match, another big Premier League match. It’s very important for us before the international break to take the three points.”