The transfer is yet to be confirmed but the winger has undergone a medical in Doha after United agreed a fee of 63m euros (£44.3m) with the French side and gave him permission to speak to them.
Argentina international Di Maria moved to Old Trafford for £59.7m last summer but was disappointing after a bright start and began only one of the last 10 games of the season.
He was left unsettled by an attempted burglary at his Cheshire home in February and has since been living in a city-centre apartment owned by former United defender Phil Neville.
Di Maria had said as recently as June he wanted to stay with Louis van Gaal’s side but failed to report for the club’s tour of the United States.
PSG manager Laurent Blanc said last Thursday the clubs were close to a deal and now the former Benfica star is preparing to put pen to paper.
Di Maria said: “I am very happy to join Paris Saint-Germain. What I know about PSG is that they are a team who have won all possible titles in France last season. They’re very important.
“They made it to the quarter-finals of the Champions League so my objective was to arrive to Paris and to help them through the quarter-final barrier, because they have struggled in the past two seasons.
“I will try to do the best I can to help the club in those objectives and reach the final stages of the Champions League.”