Pouille thrashed Steve Darcis 6-3 6-1 6-0 in the fifth and deciding rubber to see France lift the famous trophy for the first time since 2001.
Earlier, ATP World Tour Finals runner-up David Goffin dominated French No.1 Jo-Wilfried Tsonga with another straight sets victory to tie the final at two rubbers apiece.
But Belgium hopes quickly disappeared as a below-par Darcis could not muster a serious challenge to Pouille, who was engulfed by teammates after rushing through the final set without dropping a game.
"This is a feeling from another world," world number 18 Pouille said. "There are no words needed, just look at the atmosphere and hear the emotion.
"I am so proud of my team, we really wanted this trophy. After 16 years, we finally got it, I'm very happy."
The 23-year-old Pouille had showed no signs of nerves after the earlier French setback, breaking Darcis on his first service game to take the opener and three more times in the second set, the Belgian unable to repeat the sort of form that saw him shock Rafael Nadal in the first round at Wimbledon four years ago.
The third set was even more one-sided as France ended that frustrating 16-year wait, with defeats in the 2002, 2010 and 2014 finals, to win the annual competition for national teams.
A decisive doubles victory Saturday for Richard Gasquet and Pierre-Hugues Herbert had put France firmly in the driving seat, but the impeccable Goffin revived Belgian hopes with a two-hour 44 minute victory over world number 15 Tsonga.
After taking a 74-minute opening set on a tiebreak, Goffin took command to run out a 7-6 6-3 6-2 victory to set up the decider, but his heroic efforts proved to no avail although he will reflect on a season which has lifted him to seventh in the world rankings with promise of more success in the future.