The deal also includes a potential for 10m euros (£8.46m) in additional payments.
It is possible Ugarte could fly to Manchester for a medical later on Tuesday.
The move comes at the same time as midfielder Scott McTominay’s proposed 30m euros (£25.37m) switch to Napoli.
Ugarte has been linked with United throughout the summer and is now poised to sign for the Old Trafford club, just one year after joining PSG from Sporting Lisbon for a reported 60m euros.
The 23-year-old made 37 appearances for Luis Enrique’s side, including 25 in the league as PSG won their 12th Ligue 1 title.
It is understood PSG have also negotiated a 10% sell-on clause for Ugarte, with both clubs privately claiming they are happy with the deal.
The Ugarte deal is contingent on McTominay completing his switch to Napoli, although there is confidence at Old Trafford that transfer will be done.
McTominay is due to travel to Italy on Tuesday for a medical.
United sources accept the structure of the Premier League’s Profit and Sustainability regulations incentivise selling home-grown players.
Manager Erik ten Hag could not guarantee McTominay a regular start and United first accepted offers for the 27-year-old 12 months ago.
Despite that the Scotland midfielder, who first attended a United soccer school when he was five, ended up making 32 Premier League appearances and scoring seven goals for United last season.
He also started the FA Cup final victory against Manchester City.
United sources say they identified Ugarte early in the transfer window and were patient in their negotiations over a player who made the Copa America team of the tournament squad following Uruguay’s run to the final, where they were eventually beaten by Argentina.
Should the transfer go through as expected, Ugarte will become United’s fifth signing of the summer and take their overall spending to in excess of £190m.
United have spent nearly £600m on new players since Ten Hag was appointed in 2022.
