It was reported Rossi could be banned for a year, with his case handled by Italy's anti-doping agency, Nado Italia.
But at Monday's hearing the 31-year-old avoided a suspension, meaning he is free to sign for a new team and return to the pitch.
"We don't understand how this substance ended up among Rossi's foods," said Rossi's lawyer Sergio Puglisi Maraja. "There was no intentionality - the line of good faith and consistency prevailed."
"A nightmare of four months is over!" Rossi wrote on Twitter. "I only want to think about football and keep doing what I love more than anything else!"
Rossi left Genoa at the end of the 2017-18 season, during which he only managed to score one Serie A goal in nine appearances.
The talented striker then spent three years at Old Trafford between 2004 and 2007 but only made five league appearances for the Red Devils.
He has won 30 caps for Italy, scoring seven goals, but has not played for his country since a friendly against Republic of Ireland in 2014.
More recently, he recovered from an ACL injury sustained while playing for Celta in April 2017, and will now hope to find a new club following his acquittal.