Cilic's victory on Sunday meant the scheduled fifth match between Jo-Wilfried Tsonga and Borna Coric was a dead rubber.
Cilic was part of the side that lost 3-2 to Argentina in 2016 showpiece and he was ruthless in ensuring his country did not suffer another heart-breaking defeat.
Cilic delivered the final blow to dethrone defending champion France 3-1 in the final on Sunday, held at the Pierre Mauroy Stadium in the northern French city of Lille, Efe news reported.
From next year a qualification tournament will take place in February, from which 12 teams will progress to the finals in November, along with the previous four semi-finalists and two wild cards.
Pouille's level of play then dropped drastically, while Cilic kept up the intensity and broke for a 4-2 lead in the second set.
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In the second set from Tsonga was a great chance to turn the tide of the match, but when the score was 4:3, the Frenchman missed a double break-point. Two went begging but Cilic would not be denied a third time as his glorious forehand lob put the disappointment of two years ago to bed.
After Nicolas Mahut and Pierre-Hugues Herbert won Saturday's doubles to keep the tie alive, Noah restored Pouille in a bid to take down Croatian talisman Cilic.
This is the final staging of the team competition in its current format before it changes next year.
Croatia's sports-mad President Kolinda Grabar-Kitarovic was among the fans at courtside to savour a landmark title which offered some consolation after France beat Croatia in this year's football World Cup final.
"We can't wait to be in Zagreb, like the footballers when they came back from the World Cup", said Zeljko Krajan, the Croatia captain.
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Cilic lived up to his status of team leader this weekend, winning his two matches without dropping a set.
The hosts trailed 2-1 and needed to win both reverse singles on the final day to become the first team since 1939 to overturn a 2-0 deficit in a final, but their hopes of a comeback were soon dashed.
After disappearing for treatment he returned more in hope than expectation and Cilic duly sealed victory, bashing away a smash on match point.
Earlier, the 12th-ranked Coric was flawless and Chardy was powerless to counter his deep groundstrokes in the first set, dropping 14 consecutive points at one point to trail 4-0.
Yet he was never going to let Pouille off the hook.
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