The midfielder joins Inter from Dinamo Zagreb, signing a new deal to 2030.
Sucic told Inter's website: "For me, Inter is one of the biggest clubs in Europe, when I had the opportunity to come and play here I didn't have the slightest doubt.
"I really wanted to come here, for me it's a great opportunity, I know how prestigious this club is and what it represents and I'm very happy to have arrived."
Sucic, at Dinamo, played for former Italy captain Fabio Cannavaro, and also said: "He spoke very highly of it, of the Championship, of this Club because he played here, of Italy and Milan. We had a nice chat."
The young midfielder also said, "I think I can learn a lot. In this Club there are very experienced players, of a high level, who have been playing regularly in the Champions League for several years, who have played in the World Cup, European Championships, Copa America and all this confirms their great experience: I think they can help me a lot.
"Personally I can improve tactically, in defense and also in attack. You are never perfect and I believe that every day you have to try to grow and I will work hard to do exactly that."