Gambian international Barrow signs for Bologna
The 21-year-old Barrow joined the Bergamo side in 2016, coming through the youth ranks.
He scored eight goals in 51 games including a hat-trick in a Europa League qualifying match against Sarajevo in August 2018.
But after playing 22 times in the league last season he made just seven appearances for Gian Piero Gasperini's side this campaign and failed to find the net.
Atalanta finished third in Serie A last season to qualify for the Champions League for the first time.
"Thanking Musa for contributing to achieving important goals in the club's history," said Atalanta in a statement.
"We wish him the best professional satisfaction in his new adventure."
Sinisa Mihajlovic's Bologna are 13th in the league with Barrow expected to play in Sunday's game against Hellas Verona.