Yes. Italy is a founding member of the European Union. It signed the Treaty of Rome in 1957, establishing the European Economic Community (EEC), the EU's direct predecessor. Italy has been central to European integration ever since.
Rome hosts several major EU institutions, including the Food and Agriculture Organization (FAO) of the UN (though FAO is a UN agency, its headquarters location reflects Italy's pivotal role). Italy uses the euro, participates in Schengen, and holds a permanent seat on the European Council.