Kanye, who proposed to Alexis in May 2007, said: "I'm just going to go and get married - I'm not going to make a big deal out of it."
The 'Stronger' singer also revealed his model lover has been very supportive since his mother died and he is convinced he has found his perfect woman.
Kanye, who is one of three stars to appear on the cover of GQ magazine's Men of the Year issue, said: "I wouldn't get married to prove anything to anyone - it's for me, for stability in my life, and I'm so happy that I found someone that I really love, that challenges me, that keeps my life interesting, that's just as crazy as I am."
James Bond actor Daniel Craig and former US president Bill Clinton also appear on their own GQ magazine cover this month.
Kanye and Alexis spent last weekend in Paris, where the star broke down during a concert after dedicating his song 'Hey Mama' to Donda.
One audience member said: "He just cracked. He was at the end of his concert and had just started to dedicate the song and then he just lost it completely."