Paloschi scored twice in 10 Premier League games for the Swans under the guidance of Italian compatriot Francesco Guidolin.
The striker returns to Serie A, having scored 50 goals in 181 games in Italy's top flight.
Paloschi moves to Atalanta for an undisclosed fee, while his new club did not divulge the length of his contract.
"I'm really happy to finally wear the shirt of Atalanta, the team of my city," Paloschi told Atalanta's official website.
"I'm honoured by the interest that President Percassi and this club have shown in me."