Arsenal, Manchester United and Liverpool have been heavily linked with a summer move for the 24-year-old, who racked up 31 goals in all competitions this term.
However, reports in France suggest he has instead opted to remain in Ligue 1 by agreeing a five-year contract with champions PSG.
The deal is said to be worth £22million and includes a loan back to Lyon for the 2015/16 campaign.
Lacazette has recently said on his future: "I have not made my decision. I will go on holiday, leave my agent to discuss things, for him to look after all that. I am not worried.
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Alexandre Lacazette has reportedly agreed a five-year deal at Paris Saint-Germain
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"As soon as I have decided, I want it all to happen quickly. When? That is the question. I could stay at Lyon next season and have a terrible season, I could leave and have an incredible season.
"Everything depends on the destination. It would have to be for a Champions League club, you don't reject them."