A person familiar with the situation told The Associated Press that Di Maria is expected in Paris later this week to sign the deal after undergoing a medical exam in Doha on Monday.
He spoke on condition of anonymity because he is not authorized to speak publicly about the deal before it is official.
Manchester United has agreed to sell the Argentina winger for a fee that is "in the region of 63 million euros ($69 million)" the person said.
The former Real Madrid midfielder joined United for 59.7 million pounds ($99 million) last summer as the most expensive signing in the history of British football, but he had an inconsistent season at Old Trafford.
Di Maria got off to a bright start early in the season then struggled to adapt to the Premier League. The man of the match in the 2014 Champions League final was quickly reduced to a second-fiddle role in Louis van Gaal's side and ended the season with a meager tally of three goals in 27 Premier League appearances. However, his 10 assists were only bettered by Chelsea's Cesc Fabregas.
PSG, whose main goal this season is to win the Champions League, will be counting on his energy, incisive dribbles and ability to run with the ball at pace to reach a new level on the European scene, where the French champions failed to advance beyond the quarterfinals over the past two seasons.
He will give PSG coach Laurent Blanc plenty of offensive options, either on the left side of the midfield or in a more central role.