Aubameyang enjoyed another prolific season for Dortmund with 40 goals in all competitions, including the winner in Saturday's German Cup victory over Eintracht Frankfurt.
The 27-year-old has been heavily linked with the Premier League's top clubs in recent seasons including Manchester United, Arsenal, Manchester City and Liverpool.
But Aubameyang has said previously that he favoured a move to Spain, in particular Real Madrid.
However, Yahoo Sport FR say Aubameyang has agreed to join Ligue 1 side PSG in a deal worth £61million.
Chelsea and Man Utd stars make Pierre-Emerick Aubameyang's dream XI Tue, March 14, 2017
Pierre-Emerick Aubameyang has named his dream XI made up of team-mates and opponents, with Chelsea and Manchester United players featuring heavily
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Pierre-Emerick Aubameyang has named his dream XI from opponents and team-mates
I am grateful for two exciting, beautiful and eventful years. It's a pity to not go on
The Gabon international is reportedly set to earn around £8.75m-a-year.
PSG are determined to spend big this summer after failing to win the French title for the first time since 2012.
Aubameyang's imminent departure follows the resignation of manager Thomas Tuchel on Tuesday.
Pierre-Emerick Aubameyang appears to be on his way to Paris Saint Germain
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The German coach left Dortmund after rows with chief executive Hans-Joachim Watzke since their team bus was damaged by an explosion in April.
Tuchel wrote on Twitter: "I am grateful for two exciting, beautiful and eventful years. It's a pity to not go on.
"Thank you to the fans, the team, the staff and to all who have supported us."