Ibra joy and Beckham tears as PSG triumph
Sweden striker Ibrahimovic took his league tally this season to 29 goals, a personal best.
Former France forward Jean-Pierre Papin was the last player to hit 30 Ligue 1 goals in a season, for Olympique Marseille in 1989/90.
Ex-England skipper Beckham, who will retire at the end of the season, broke down in tears when he was substituted by Ezequiel Lavezzi in the 81st minute.
Beckham, who was named skipper against Brest, was hugged by his team-mates as he left the pitch to a standing ovation having set up Blaise Matuidi for the second goal.
It was the former Manchester United midfielder's 10th league appearance for PSG and it is not yet clear whether he will take part in the last game of the season at Lorient next weekend.
Beckham was the second-last player to get to the centre of the pitch where the players and staff were presented with the league trophy.
'Hello, Goodbye', a Beatles song, was played over the public address system as a film showed highlights of his time at the club before Beckham walked towards the podium with a St George's flag wrapped round his shoulders.
"I want to say thank you to everybody in Paris, to my team-mates, to the staff, to the fans," said the 38-year-old former Real Madrid and Los Angeles Galaxy player. "To finish my career here could not be any more special.
"I want to enjoy my family now, I have all the souvenirs I want now so I'm very, very happy. Merci Paris. I'm very sad to be leaving but thank you."
On Monday, title celebrations on the streets of Paris turned sour when 30 people were injured in clashes between fans and police in the west of the French capital but the atmosphere was good against relegated Brest.
Elsewhere, second from bottom Nancy were relegated after a 2-1 home defeat by Bastia left them five points from safety.
Emotions also ran high at Montpellier as Rene Girard, the coach who led them to their first Ligue 1 title last season, said farewell to the fans after announcing earlier this year that he was leaving.
Eighth-placed Montpellier drew 0-0 against Lille who are fifth and received a severe jolt to their hopes of playing in next season's Champions League.
With 61 points, Lille trail third-placed Olympique Lyon by two points.
Lyon, whose visit to sixth-placed Nice was put back 24 hours until Sunday due to heavy rain, are one point ahead of Saint-Etienne after Les Verts won 2-0 against Olympique Marseille.
Marseille are 10 points behind PSG and assured of second spot. The top two qualify for the Champions League while the team in third go through to the preliminary round of the competition.
Most of the PSG players had dyed their hair red and blue and started the game brightly against Brest in front of a crowd of 44,983 that included Beckham's wife Victoria and mother Sandra.