The Super League leaders came back from 10-0 down to defeat Warrington Wolves.
A victory parade started at the KCOM Stadium in Hull, before travelling through the city and greeting fans at Queens Gardens for a party.
Hull's previous Challenge Cup win was over Leeds in Cardiff in 2005, while Wembley was being rebuilt.
Fans lined the streets on Ferensway, Prospect Street, George Street and Wilberforce Drive as two open top buses carrying players and club staff passed.
Supporter Ashleigh Charles said: "I didn't think anything could top Cardiff, but for me it was watching my dad see his team win at Wembley.
"It's all I've ever wanted, to share it with him, so it was the best day of my life by far."
Stephen Brady, leader of Hull City Council, said: "After so many years of trying, Hull have finally triumphed with a gritty, determined display at Wembley.
"They're a credit to themselves, to the club and to the city, they've done a great job."
Hull-born player Kirk Yeaman said: "Obviously it means a lot to the fans, to the players, staff and everyone involved in Hull FC."
"It's the best thing I've had in my career," he added.
Thousands of people welcomed home Challenge Cup winners Hull FC back to the city after their win in Saturday's final at Wembley.