Italy, stuck in recession, hopes the fair will be a big money-spinner. Ten million tickets have been sold already for the six-month event.
But shortly after the opening, protesters in Milan clashed with police, who responded with tear gas.
Representatives of 145 countries are in the city for the fair, which boasts 54 national pavilions at a sprawling site.
The food theme focuses on nutrition and combating hunger globally. But it is also a showcase for Italian cuisine.
The exhibition has already been marred by scandal after several officials in the organising body were arrested for corruption.
And violence broke out on Friday as dozens of people protesting against the Expo torched cars and broke shops windows.
Some groups have criticised the fair, calling it a symbol of big business interests, and held protests.
There was an anti-globalisation march by students in Milan on Thursday.
Pope Francis, who spoke via a televised link-up to the opening ceremony, said he wanted every person who visited the Expo to think of the "faces of millions of people who are hungry today".
Meanwhile Italian Prime Minister Matteo Renzi said: "Today it is as though Italy is embracing the world."
Italy hopes the fair, covering a one million sq m (10.7m sq ft) site, will attract some 20 million visitors and generate revenues of about $10bn (Â£5.6bn; â‚¬8.9bn).
A major global commercial fair - Milan Expo 2015 - has opened in northern Italy with food as the theme.