"We can finally say we are champions. I'm very proud of this team, of these players. It's a dream for me, I'm very happy," Monaco skipper Radamel Falcao told Canal+.
Monaco's 11th straight victory took them up to 92 points, six ahead of PSG, and they can match PSG's record of 30 wins in Saturday's final game at Rennes.
"We've been able to hold on all the way against teams like Paris and Nice who kept up with the pace until the end," said Mbappe. "Unfortunately for them but luckily for us, we're the ones leaving with the trophy."
Not since Claude Puel guided a squad featuring Fabien Barthez, David Trezeguet and Willy Sagnol to the 1999-2000 title had Monaco been crowned kings of France.
Saint-Etienne held Monaco to a 1-1 draw in October, but Christophe Galtier's side arrived in the principality low on confidence after their 5-0 thrashing by PSG and decimated by injury.
Mbappe struck when he latched onto Falcao's threaded pass and calmly rounded the Saint-Etienne goalkeeper before slotting home.
Monaco did not display their habitual fluency which has led them to become only the fifth team to score more than 100 goals in a French season.
Germain, who was with the club in 2011 when Monaco were languishing at the foot of the second divison, should have sealed the victory on 74 minutes when Mbappe slid the ball across the six yard area only for him to squander the chance.
But the 27-year-old striker made amends in stoppage time with a tap-in.
"We've had a superb season both individually and collectively. I think we fully deserve it," said Germain. "This year we've been uncompromising. You have to congratulate the whole group and especially everyone in the ground who was magnificent."
Jardim, who has won championships in Greece and Portugal, said: "This is the biggest title in my career. We've won with a team that wasn't one of the favoruites. But we've been better than the rest. We've had a geat season."
Since heading the league during the fourth and fifth round of matches, Monaco have not been outside the top three. They went first following a 4-1 demolition of Marseille in January and have maintained their post at the summit since then.
"I'm proud of what we have done and I want to thank my family for all their support," added Jardim.