The Frenchman completed a permanent switch to San Siro from Valencia on Saturday, after spending the second half of the previous campaign on loan at the club.
Milan endured a hugely frustrating season last term, slumping to an eighth-place finish in Italy's top flight, some 45 points adrift of winners Juventus and outside the qualification places for European football.
However, Rami is confident that the good times can return to the club, starting with a return to the continent's premier competition.
"We cannot forget what Milan have done, as we can write history again, the one that I and the club want," he told reporters outside Milan's training ground.
"I feel lucky and I tell myself that every day, that is my strength. That's why I can believe in the Scudetto... I know anything is possible, but first of all we should focus on Champions League qualification."
Milan are a team set to begin a new era under the stewardship of incoming head coach Filippo Inzaghi.
And France international Rami - who penned a deal until June 2017 - is thrilled to be staying in Milan.
"I am very happy to be at a great club like Milan," he continued. "I wanted to prove how much I wanted to stay here, I saw the fans supported me and that gave me the strength to do everything possible."
‘After Manchester City’s recent form, maybe they’re the underdogs against Manchester United!’ Former Red Devils defender on this weekend’s derby
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
