"The world is saluting Trump's election," Mr Renzi said.
"In Italy's name I congratulate him and wish him well for his work, convinced that our friendship remains strong and solid.
"This is a starting point for the whole international community; it's a new political development which, along with others, show that we are in a new season."
The premier had, however, previously stated that he hoped Mr Trump's Democratic rival, Hillary Clinton would win.
On the other hand, leader of the Northern League, Matteo Salvini, has hailed Donald Trump's triumph as the "revenge of the people".
"It's a blow to globalization," Mr Salvini told the League's Radio Padania.
"It's a win for courage, pride and labour and security issues against the banks, speculators, journalists and pollsters.
"The people have beaten the powers that be 3-0."
The right-wing leader added that his party, which, like Mr Trump, takes hard-line stances on migration, should follow the lead of the US president-elect.
"It's time to be more daring," he declared.
Meanwhile, former Italian premier Enrico Letta has described Mr Trump's win as the biggest political development since the fall of the Berlin Wall.
"The greatest political break since the fall of the Berlin Wall. A big wake-up call for Europe," he announced via Twitter.
Italian Foreign Ministry Undersecretary Benedetto Della Vedova has shared his concerns that Mr Trump's victory means that Europe is now more alone than ever.
"The United States will survive Trump," Mr Della Vedova said.
"My concern is what will happen in our home; as of tonight, Europe is more alone and I don't think it's equipped to be so.
"We will have a political season in which everyone will be a little Trump, isolating one EU country from another and making Europe weaker at a time in which we will be called on to play a crucial match for democracy, tolerance, multilateralism and international trade."
Mr Trump is set to take office on January 20, 2017.
With ANSA
