The midfielder has joined the San Siro club on loan from Genoa, but wants to stay at the Serie A giants beyond the 2012-13 campaign
The 25-year-old was snapped up from Genoa on a one-year loan deal after Sulley Muntari sustained a serious knee injury, and Constant is desperate to show he has got what it takes to succeed at the highest level.
"I know that I am here because of Muntari's injury but I still want to play and win. I will give 100 per cent for the team. Now I have to prove that I am as good as my team-mates. I will try my best," Constant stated at a press conference.
"I am ready. I have to play with lots of personality, give 100% and even more. It is important for me to show that I want to stay here.
"My dream came true when I came here, the competition is so high but I am ready to play and fight for my place. You have to be perfect here at Milan and I will have to work harder than ever."
The versatile midfielder then went on to discuss the departure of Thiago Silva to Paris Saint-Germain, and the imminent transfer of Zlatan Ibrahimovic to the same club, and stressed that Ligue 1 will be a positive experience for the duo.
"We all know that Ibra and Thiago Silva are world-class players, but if they go then other players will arrive to replace them.
"The French league is a lot more physical compared to the Italian league, where tactics are more important, but it is growing. If they do go to the Ligue 1 then it will a positive experience for them."
Thiago Silva signed a five-year deal with PSG on Saturday, with Ibrahimovic expected to follow suit in the upcoming days.