The 34-year-old has helped Atletico lift the Copa Libertadores and the Recopa Sudamericana - having turned down Besiktas in January to sign a new deal.
A World Cup and Ballon d'Or winner previously in his career, Ronaldinho has been with Atletico since 2012 when he arrived from Flamengo.
However, Culpi confirmed the forward is to leave the club following their Recopa success against Lanus last week.
"I can't call on Ronaldinho anymore," Culpi told SporTV.
"His cycle with us has ended.
"It's unfortunate because he's an idol to all of us. Everyone loves his football, the way he plays and he's a very charismatic person.
"But that's the way it goes. He's leaving and we must move on without him."
The former Barcelona and Milan player has been linked with a move to Boca Juniors, where he could serve as an ideal replacement for Juan Roman Riquelme who returned to Argentinos Juniors recently.
‘Sir Alex told Van Persie to watch my goal back at Anfield for some shooting tips! It was a beautiful goal, though. It’s a shame that I didn’t do it more often’: Manchester United cult hero recalls stunning strike against Liverpool
‘So many times when we played Manchester United, arguments would start before the first whistle had even blown – the players would try to kill each other with their eyes’ Former Arsenal star remembers famous Premier League rivalry
