"The documents were registered at the Italian Football League's offices this morning. Inter thank Adriano for his 74 goals and the eight years spent together."
The move was widely expected with the 27-year-old's contract due to run out at the end of next season.
Adriano, who has long been troubled by alcohol and personal problems, decided not to return to Italy at the start of the month following Brazil's World Cup qualifiers.
He said he had lost the pleasure of playing and did not want to return to Italy and added he would stay in Brazil to rethink his career.
Inter coach Jose Mourinho overlooked the striker at the start of the season but he worked his way into the first team and helped Inter surge ahead at the top of Serie A, where they are close to sealing a fourth straight Italian title.
When he did not return from Brazil, Mourinho sympathised with Adriano rather than berate him like he had in the past.
The end of the contract makes it highly likely that Inter will buy at least another striker in the close season.
Forwards Julio Cruz and Hernan Crespo will also probably leave while top scorer Zlatan Ibrahimovic has expressed his frustration at Inter's continued failure in the Champions League and could be a transfer target.
Inter have been linked in the media with Chelsea striker Didier Drogba, Genoa forward Diego Milito and Sampdoria playmaker Antonio Cassano.
