After beating Lille 4-0 and surpassing 100 league goals on Sunday, Monaco knew a draw would be enough to end Paris Saint-Germain's four-year dominance of Ligue 1.
And Monaco were put on track to claim their eighth league title when Mbappe gave his side the lead after 19 minutes, beating the offside trap and racing on to a sublime pass by strike partner Radamel Falcao to score.
Mbappe's 12th league goal since the start of February ensured Monaco have now scored in 31 successive league games - a Ligue 1 record for a single season.
Leonardo Jardim's men added to the party mood at Stade Louis II with a second goal in added time, substitute Germain tapping into open goal to secure a 10th successive home victory.
Monaco move six points clear of deposed champions PSG and will finish the season with 95 points if they win their last game of the campaign at Rennes on Saturday.
Alexander Soderlund and Habib Maiga had early efforts for Saint-Etienne as Monaco made a nervous start to the game.
Ligue 1's newly-crowned Young Player of the Year Mbappe had Monaco's first chance after 17 minutes, but the striker's powerful shot was beaten away by goalkeeper Stephane Ruffier.
The teenager would not be denied moments later, however, as he sent Monaco on their way to glory.
Falcao's throughball was perfectly timed for Mbappe to beat the offside trap, run clear of the Saint-Etienne defence, round Ruffier and slot in his 15th Ligue 1 goal of the season.
The duo were both involved again as Monaco almost doubled their lead on the half-hour mark, but, after Ruffier could only parry Mbappe's shot, Falcao saw his rebound effort blocked.
Falcao whipped a 30-yard drive narrowly over the crossbar and Thomas Lemar hit an ambitious effort just off target shortly after the interval as Monaco sought to extend their lead and make certain of their title triumph.
Ruffier then dived low to his right to turn a Falcao header around the post as Jardim's side continued to press, before 18-year-old Arnaud Nordin was denied by Danijel Subasic after breaking rapidly down the right wing from inside his own half.
Monaco's focus slipped as the minutes ticked away and Germain somehow shot wide from six yards after swapping passes neatly with Mbappe.
That lapse was quickly forgotten as Germain made amends, tapping home Lemar's pass with the last kick of the game to ensure Monaco recorded their 29th league win of the season and secure a famous title triumph for Jardim and his players.