The banned former UEFA President and FIFA vice president said in a statement it was “the end of a long nightmare for my family and those close to me”.
Since September 2015, the former France midfielder has had the status of “between a witness and an accused person” in criminal proceedings opened against then-FIFA President Sepp Blatter.
No criminal case was ever opened against Platini.
The investigation was related to Mr Blatter authorising FIFA to pay Platini $2m (£1.5m) in uncontracted backdated salary in 2011.
FIFA’s ethics committee also investigated Platini’s request to FIFA for pension contributions he was not entitled to.
Blatter agreed to the request and added more than $1m to Platini’s retirement fund.
Platini, 62, was banned from football for four years until October 2019.
Both he and Blatter denied any wrongdoing but Court of Arbitration for Sport judges refused to overturn the bans on both of them.
Platini was sacked as UEFA president and barred from trying to succeed Blatter as FIFA president in 2016.
Former France captain and coach Platini said: “I will come back: where, when, how? It’s too early to say. But I will come back into football.
“Because football is my life and I deny anyone the right to deprive me of my life.”
He said he now hoped FIFA would lift his ban.
“My legal advisers will take all the necessary measures to ensure the FIFA suspension is lifted,” he said.
The Swiss public prosecutor’s office said that although no evidence had been found “so far” to bring charges against Platini, the investigation was “not completely over”.
He could still be required to appear before a judge if new evidence was found in the case, a spokesman for the prosecutor’s office said.
The investigation concerns the activities of Blatter during his 17-year presidency of FIFA.