Marin Cilic beat Lucas Pouille in straight sets to secure Croatia's second-ever Davis Cup title.
Cilic beat Pouille 7-6, 6-3, 6-3 to give them an unassailable 3-1 lead over hosts and defending champions France.
France had pushed the final into a third day after Nicolas Mahut and Pierre-Hugues Herbert won Saturday's doubles rubber.
"It's not every day that you become a world champion," 30-year-old Cilic said.
"For us it's a dream come true, for this nation. You can see the fans are so passionate and they are here enjoying themselves. In Croatia it's going to be incredible too.