Ospina, who has 44 caps for Colombia, rose to prominence with some impressive performances at the World Cup, where his team lost to hosts Brazil in the quarter-finals.
And following Nice’s 3-2 friendly defeat to Brentford in London on Saturday, Nice manager Puel told Sky Sports that Ospina, 25, had agreed to join the North London club.
"It is confirmed, yes," Puel told Sky Sports News. "At 25 years old it is important for him to experience another championship, so it is a fantastic move for him.
"I think he can take the number one spot at Arsenal because his qualities are very, very strong.
"He is very good with his feet, with his arms, and he knows football. He is a very, very good player."
There is no word from Arsenal but Ospina, available at a cut-price £3million, had looked to be on the brink of moving to the Emirates Stadium after Arsene Wenger let slip that the player would be number two to Wojciech Szczesny.
"You know at the start Szczesny will be the number one, then again we'll be down to performances and, if Ospina shows that he is better, he will play," the Frenchman had told ESPN on Friday.
Ospina will be the third World Cup star to arrive at Arsenal this summer, joining Chile’s Alexis Sanchez and France’s Mathieu Debuchy, who left Barcelona and Newcastle United respectively.
Wenger's side, who won the FA Cup and qualified for the Champions League last season, have also been linked with Southampton duo Morgan Schneiderlin and Calum Chambers, although a move for Real Madrid's Germany midfielder Sami Khedira appears to have stalled.