"God knows how long our journey had been," forward Jeremy Menez, who scored the winner, told French TV channel Canal Plus. "It has been a great season and tonight we got our reward."
Right back Christophe Jallet, the only player in Sunday's starting lineup at the club when Qatari investors QSI took over two years ago, broke down in tears after the final whistle.
"We had to fight throughout the season. We experienced some hard times. We're very happy to win this title together and we'll celebrate it the right way," he said.
Big-spending PSG, who were expected to dominate Ligue 1, showed signs of nerves in recent weeks, collecting four red cards in two games and failing to beat lowly Valenciennes in Paris last weekend.
"We knew we were close but it was hard," said goalkeeper Salvatore Sirigu, who was serving the second of a two-game ban on Sunday.
"It's the first title for many of us. We hope it's just the first of many," added Sirigu, who joined from unfancied Italian side Palermo two years ago.
Sunday's victory gave PSG a seven-point lead over second-placed Olympique Marseille with two games to play.
"It's a relief," said midfielder Blaise Matuidi. "The truth is that it has not been easy. We were expected (to win the league). The title was our goal. We did it."
"I'm so pleased to be part of this team, with great players like Zlatan (Ibrahimovic) and Thiago Silva," added the France international, named on a four-man short-list for the Ligue 1 Player of the Year award with the two former AC Milan players.
Only Ligue 1 leading scorer Ibrahimovic, the first player to net 27 goals in a season since Jean-Pierre Papin during the 1991-92 campaign, did not appear in the mood to celebrate.
Ancelotti told a news conference the Sweden striker was frustrated at being summoned to anti-doping tests while the rest of the squad basked in the glory of winning the title.
Ibrahimovic will, however, be able to celebrate on Monday when the players are due to be greeted by fans at the Trocadero place, near the Champs-Elysees, where they will be handed the French league trophy for the first time since 1994.