Leverkusen beat Werder Bremen 5-0 to move 16 points clear of Bayern Munich – who have won the last 11 Bundesliga titles – with five games left to play.
It is the first trophy Leverkusen have lifted since their German Cup victory in 1993.
Incredibly, Alonso’s side remains undefeated in all competitions and on course for a historic treble.
Leverkusen holds a 2-0 advantage over West Ham ahead of Thursday’s Europa League second leg and will face second-division Kaiserslautern in the German cup final.
Against a backdrop of expectation and a cauldron of noise at the BayArena, Alonso’s side extended their unbeaten streak to 43 matches.
Wave after wave of attack followed but Leverkusen were thwarted until Granit Xhaka curled home a left-foot strike from 25 yards on the hour to effectively end any hope of Bremen spoiling the party.
Wirtz, introduced on the stroke of half-time, then rifled high into the net from a similar distance midway through the second half and a brief pitch invasion followed when he bagged his second in the 83rd minute after going clean through on goal.
He had his treble with a fine finish, the last kick of the match which sparked another pitch invasion as Leverkusen got the victory they needed to guarantee the title with five matches left in the season.
