If your boyfriend truly loved you, he'd be willing right now to sacrifice anything that got in the way of that love–including his drinking.
This may not be the answer you hoped I'd give, but right now all you have from him is an empty promise–and one I seriously doubt he will keep. Almost every week, I get at least one letter from someone who was once in your situation, and went ahead and got married in spite of the advice of others. Almost without exception their life has been marked by unhappiness, broken promises, abuse and alcoholism.
Instead, I urge you to seek God's will for your life, including the person He has chosen for you to marry. God loves you and doesn't want you to become trapped in a relationship that holds little hope of peace and stability. As a first step, turn to Christ and commit your life to Him as your Savior and Lord. The psalmist's experience can become yours: "You have made known to me the path of life; you will fill me with joy in your presence" (Psalm 16:11).
Then challenge your boyfriend not just to stop drinking but also to give his life to Jesus Christ. He needs Christ's presence in his life, and he also needs Christ's power to deal with whatever problems he has that make him turn to alcohol. Don't be satisfied with anything less than God's best for your marriage.