The 30-year-old - who has previously played for among others Barcelona and Juventus - will be paid a reported €15 million ($18.4 million) a year, making him the highest-paid player in Ligue 1, should he pass a medical on Wednesday morning.
He will then be officially unveiled at a press conference at on Wednesday afternoon.
Leonardo - a former player and coach of AC Milan - had finalized the deal with more talks on Tuesday after intensive negotiations last Thursday and Friday with the cash-strapped Italian giants willing to sell for the right price.
"We've reached agreement, the deal is done: Zlatan Ibrahimovic is one of our players, he'll write history for Paris Saint-Germain," Leonardo was quoted as saying by Italian daily La Gazzetta dello Sport on their website.
The Brazilian was quoted by L'Equipe as rejoicing at attracting "a player of real calibre", and by Parisien as a player who is able to "change everything".
It will take Qatari-owned PSG's spending to over €100 million ($122.7 million) in the close season and to around €173 million since Qatar Sport Investments (QSI) bought the historic club almost a year ago.
Ibrahimovic's arrival along with AC Milan defender Thiago Silva – who signed last week - comes at an estimated cost of between 70 and 80 million euros while they have also signed in the past couple of days young Italian defensive midfielder Marco Verratti from newly-promoted Serie A side Pescara for €11 million.
PSG - who will play in the Champions League next season after finishing second in the league last term - also shelled out a reported €30 million for Argentine international Ezequiel Lavezzi from Napoli earlier this month.
Signing high profile players like Ibrahimovic will come as some relief to Leonardo who had seen earlier efforts to sign Brazilian striker Alexandre Pato (AC Milan), Argentinian Carlos Tevez (Manchester City) and another Argentinian Gonzalo Higuain (Real Madrid) come to nothing.
The fees being paid out and the salaries being promised have provoked some disgust in France with former Minister for Sports Roselyne Bachelot expressing her 'indignation, almost disgust' on French TV on Tuesday.