The former Manchester United winger has left Paris Saint-Germain after a seven-year spell in France.
He scored a farewell goal in his final PSG game before leaving the field in tears in May.
As speculation about his future grew, the 34-year-old Argentinean revealed that his wife would assist him in making a decision.
Last month, it was reported that he had rejected the first offer from Juventus after Barcelona expressed interest.
In their first attempt, Juventus offered Di Maria a two-year contract when he only wanted a one-year contract.
According to transfer guru Fabrizio Romano, the veteran attacker appears to have gotten his wish and is about to make his move to the Serie A club official.
“Angel Di Maria to Juventus, here we go!” he tweeted.
“Agreement reached on a free transfer; Di Maria is set to fly to Italy this week.”
“One-year contract for Di Mara – docs are being prepared for signing soon.”
Di Maria joined PSG from Manchester United in 2015 and has played an important role under Laurent Blanc, Unai Emery, Thomas Tuchel, and Mauricio Pochettino.
Last season, the 121-time Argentina international appeared in 30 games for PSG across all competitions, scoring four goals.
He has made 294 appearances for Paris Saint-Germain, scoring 91 goals.
He won the Ligue 1 title five times at Parc des Princes, as well as the French Cup five times.