"He's re-signed!" Atletico's president Alexandre Kalil announced on Twitter.
Besiktas said at the end of last month that they were keen to sign the 33-year-old Ronaldinho but admitted they needed extra sponsorship to meet his wage demands.
The former Barcelona and AC Milan midfielder joined Atletico in June 2012 and won the Copa Libertadores with them a year later, the first time he or they had lifted South America's biggest club competition.
He showed glimpses of the football that made him FIFA's World Player of the Year in 2004 and 2005 and was recalled by Brazil when Luiz Felipe Scolari took over 14 months ago.
But he failed to make an impression at international level and looks unlikely to make Brazil's World Cup squad.
Neither Atletico nor Kalil gave any details of the new deal or said how long the contract was for. (Reporting Andrew Downie, editing Tony Goodson)
- Sports & Recreation
- Atletico Mineiro