The veteran striker left Inter Milan for the Zebrette last week.
At the club's new season ceremony yesterday, Alexis declared: "I was 18 years old when I arrived here, Udinese was my first family, the last day here we were in the Champions League, it was beautiful.
"I came back and found great players, a great captain, we can do something good, we are waiting for you all at the stadium."
New Udinese technical chief Gokhan Inler also said: "Thank you very much for the chants, I'm excited, thanks to Udine, this year I have the responsibility of bringing Udine back to the levels we know, we are a family and everyone will give their contribution.
"I have always had good memories of Udine, I want the team to get back to the top, we are a family and it must be strong. The fans? They are very important to us, Udinese is that way thanks to them."