Why has Gatsby bought his house on the West Egg?

To be close to Daisy.

Gatsby moves into the house in West Egg so he can be across the lake from Daisy. When he is out alone at night "reaching into the distance" he is reaching towards the green light of Daisy's dock; the green light represents Gatsby's dream of being with Daisy (green is a very large symbol throughout the book). Gatsby also buys the house because it is huge and shows off his new money. This is another attempt to impress Daisy and win back her love.