Milan finished the 4km event in three minutes and 59.153 seconds, beating Charlton's time of 3:59.304, which had broken Filippo Ganna's 2022 record.
"We didn't get distracted by Charlton's world record this morning. We just tried to stick to the schedule we had set ourselves and things went great," Milan told Italian media.
"Before the final I wasn't so sure I could do it. Charlton's time was incredible and I am still in disbelief that I beat him."
Britain's Charlton, who clocked 4:00.232 in the final, took silver as Milan claimed his maiden individual pursuit gold at the World Championships after winning two silvers and one bronze in previous editions.
The Italian has also won gold medals in team pursuit at the 2021 World Championships as well as the Tokyo Olympics. He also took bronze in team pursuit at this year's Paris Olympics.
"An evening of celebration? No, this performance deserves much more," Milan added.
