The Brazil international's future appeared in doubt after the arrival of head coach Luis Enrique, with French champions Paris Saint-Germain thought to be waiting in the wings for his services.
As he enters the final year of his contract, Alves intends to "continue working" with Barcelona and help them challenge both domestically and in Europe next season.
The 31-year-old arrived back in Spain on Tuesday following Brazil's humiliating end to the FIFA World Cup and outlined his desire to stay with the club.
"I want to fulfil the contract I signed," he is quoted as saying by Marca. "I am very happy at the club.
"We have had some wonderful years, the last less so, but I am back to enjoy this club.
"It is not only my decision, though, my aim is to fulfil the contract I signed, but it must be by mutual agreement."
Alves joined Barca from Sevilla in 2008 and has won four Liga titles and the UEFA Champions League twice during his six years at the club.
