You remember the story of The Deathly Hallows; further stories indicate he Elder Wand passed from hand to hand by combat. Albus Dumbledore possessed the Elder Wand. You defeated him; disarmed him and had him at your mercy. I -- think the wand's loyalty transferred to you.

[Little does he know that it went to Harry after he got disarmed in Malfoy Manor; he hasn't put that scuffle into the puzzle. Even Snape can occasionally miss a detail.]