Dan Ndoye scored the only goal in Rome’s Stadio Olimpico, latching on to a loose ball in the box before lashing a shot into the back of the net.
It secures Bologna a place in next season’s Europa League, with Milan – who have not won the Italian Cup since 2003 – still uncertain of a European place.
Bologna, captained by Scotland midfielder Lewis Ferguson, will feel they deserved their victory.
Ex-Hamilton and Aberdeen man Ferguson fired a shot over the bar in the first half from outside the box.
Milan thought they were going to take the lead before the break but a Lukasz Skorupski double save, including to deny Luka Jovic from close range, kept them out.
And in the end Switzerland international Ndoye was the hero. Bologna had not won any major silverware since this trophy 51 years ago.
It was the first major honour for their manager Vincenzo Italiano, who lost three finals in the previous two seasons with Fiorentina.
“We deserved this, especially as we played great tonight. It was a fantastic performance,” said the 47-year-old.
“We’ve crowned an incredible year with the cup, which is what our fans deserved.”
Last summer Italiano replaced Thiago Motta, who left for Juventus, as Bologna boss. Juve sacked Motta in March.
Juventus, Inter Milan, Napoli and Lazio had won every Italian Cup between them since 2008.
Milan manager Sergio Conceicao, who is under pressure with his side eighth in Serie A, said: “Right now I have a lot of thoughts about the game and what I did, what went right and what went wrong. I didn’t get into football a couple of days ago.
“I’m trying to work out what more we could have done tonight. We’ll finish the season with dignity and we’ll talk about my future later.”
