The initial fee for the 23-year-old is €105m (£89m; $116m), but the figure will rise depending on his success.
The figure stands in stark contrast to other newly-released statistics in Italy.
According to the statistical body Instat, the number of people living in absolutely poverty in Italy has risen to its highest point since 2005, with 7.6% of the population affected.
The figures, released last month, showed that 4.6 million people were now unable to afford goods and services "essential to avoid grave forms of social exclusion".
Italian media said some of the change could be attributed to migrant families, almost a third of whom live in absolute poverty. More than 153,000 migrants arrived in Italy last year.
Back in 1992, when AC Milan broke the world transfer record to sign Gianluigi Lentini, the Vatican condemned the £13m fee, calling it "an offence to the dignity of work".
There's been no comment from the Vatican this time around.
We broke down Italy's poverty levels relative to the cost of Pogba.
Pogba's salary at Old Trafford has not been publicised, but it is believed to be about €12m a year.
When the poverty figures were released last month, Massimiliano Dona, secretary of the National Consumers' Union, called them "a national disgrace" which showed the government had "not done anything to reduce inequalities and help those most in need", La Repubblica reported.
Economy Minister Pier Carlo Padoan told the Ansa news agency the government was committed to bringing more people out of poverty, but it faced the worst financial situation in 20 years.
Prime Minister Matteo Renzi was appointed in 2014 after a promise to bring life back into the economy, but little improvement has been seen.
He is also facing pressure over a referendum he has called for later this year to cut the powers of the Italian Senate as part of a series of planned constitutional reforms.
Mr Renzi has promised to resign if he loses the vote.
After weeks of speculation, French footballer Paul Pogba has completed a world record transfer to Manchester United from Italian club Juventus.