Luis Enrique capped his first season as Barcelona's head coach by matching Pep Guardiola's feat from the 2008/09 season when the Catalans captured the European, Spanish league and cup titles.
An early goal by Barca's Ivan Rakitic late last night was cancelled out by Juventus' ex-Real Madrid striker Alvaro Morata, who equalised on 55 minutes.
But Suarez put the game beyond the Italian champions with a 68th minute strike off a rebound at Berlin's Olympic Stadium. Neymar added the third with the last kick of the game in the 97th minute.
This was the fifth time Barcelona have been crowned European champions and it is their fourth Champions League title in the last decade after their 2006, 2009 and 2011 triumphs.
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On the streets of Barcelona, where you could have heard a pin drop during the final, thousands of ecstatic fans dressed in their team colours of blue and red celebrated with cheers, chants and fire crackers.
"It's a dream, I still can't believe it!" said Eduard Ocana, a 23-year-old student, in the Catalan capital, as cries of "champions, champions!" echoed around the famous party street of Las Ramblas.
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For Suarez it was a triumphant end to a first season with the Spanish champions after his ignominious biting ban at the World Cup.
"It's incredible, it's something unique. To win these trophies you have to suffer," he said.
"The best thing about this side is the spirit and the fact we've been united since the start of the season.