Rapper Buys Back To The Future Shoes For $37.5 K

TMZ spoke with Tinie's rep ... who told us the London native is a serious shoe freak ... and he simply fell in love with the Marty McFly sneakers at the auction in L.A. last night.

We're told Tinie -- whose new song "Written In the Stars" has become a worldwide hit -- is on his way to South Africa at the moment.