The French champions, who had their Financial Fair Play restrictions lifted by UEFA last month, have paid 63 million euros for Di Maria according to local media reports.
The fee is just short of the 64 million euros (45.07 million pounds) Ligue 1 record set by PSG when they bought Uruguay striker Edinson Cavani and the more than 60 million that Monaco paid for Colombia striker Radamel Falcao in 2013.
“I know that PSG has a very important, very good project … to win the Champions League... this is what I share with it. I want to bring the maximum … to go beyond the quarter-finals," Di Maria told a news conference at his unveiling in Paris.
PSG have failed to get past the last eight in the Champions League for the last three seasons but with former Real Madrid winger Di Maria, Laurent Blanc's side will hope to go further.
“We have the right team to do better, to win the Champions League," said PSG president Nasser al Khelaifi. "We know it’s very tough but we want to try and win it, especially now that we have one more player that has won the Champions league."
The 27-year-old Di Maria, who was looking to end a disappointing stint at United, could partner fellow Argentine Javier Pastore, the duo having been impressive in helping their country reach the final at this year's Copa America.
Di Maria is expected to play on the left wing, which would send Cavani to the right flank with Swede Zlatan Ibrahimovic playing as a lone striker.
Neither Ibrahimovic nor Cavani have won the Champions League but Di Maria was man of the match in the 2014 final when Real Madrid lifted the trophy with a 4-1 win over Atletico Madrid.
He was also instrumental in Argentina's campaign at the 2014 World Cup, where the Albiceleste reached the final.
After an impressive start at Old Trafford last season, with three goals in his first four games, he suffered a two-month injury layoff and failed to score again in the league.
Towards the end of the season he was regularly left out by manager Louis Van Gaal, who became resigned to the club taking a heavy loss on the Argentine after shelling out a British record fee of almost 60 million pounds 12 months ago.
Di Maria did not join United's pre-season tour of the United States and on Monday travelled to Doha, Qatar, where PSG's owners are based, before finalising the deal.
(Additional reporting by Ingrid Melander in Paris and Steve Tongue in London; Editing by Ken Ferris)
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