The striker worked with the Portuguese manager at Inter Milan seven years and is relishing the prospect of linking up again.
"I have great memories," said Ibrahimovic. "The only regret I had with Jose was that I had a short time with him.
"I had one season. We won together, we enjoyed it together and had a great time together. I learned a lot, and I got to know him as a person, not only as a coach, and only positive things.
"He's a winner, I'm a winner and we know both what we want. We want to win. Wherever we go, we win. And we will win."
Ibrahimovic started his career at Malmo in 1999 and has won an array of titles, including four league champiobships.
But up until now he had never played for a Premier League club and he admits, quite modestly, that it won't be easy.
He said: "I think it's a big challenge for me. Wherever I came I won, and I'm looking forward to this new adventure, a new chapter in my career, in my life.
"If I could win here, I don't know how many players have had the possibility to play in different competitions like I have and at the same time be winning.
"So I will work hard. I know my mentality, I know what I want, I come to win. I want to win, but behind everything is hard work. That is what we have been doing so far, and that is what we come to do here also."