The same reason that Olympic champions weep when they're on the winner's podium - years and years of hard work and blood/sweat/tears have culminated into them being the best in the world at what they do - it's a release of emotions.
Against all the odds, Wade has beaten the worlds hardest contest after years and years of effort against the rest of the world.
He's also saved the oasis from IOI, he's met (sort of) his idol (Halliday), he's rich and powerful beyond his wildest dreams, and he's ensured the safety of his newly found love (as well as saving the lives of the rest of his friends).
So yes, it's a fairly emotional moment....
...or he just stepped on a LEGO brick, this generally brings a tear to anyone's eye.