Muriel, whose contract with Atalanta was set to expire on June 30, will play in MLS this season.
Prior to his departure, he posted on Instagram a video message bidding farewell to Atalanta fans.
He said: “I already wanted to thank you so much for the four and a half wonderful years that I lived in Bergamo…
“Bergamo will always remain in my heart, like a second home.
“Thank you for all the messages of affection these days, I hope you will follow me with sympathy also in my new adventure in Orlando.”
Muriel, 32, scored 68 goals in 184 appearances for Atalanta, the club he joined from Sevilla in the summer of 2019.
At Orlando City, Muriel will work under fellow Colombian Oscar Pareja.