TileMill and MapBox

TileMill is a pre-built application containing the Mapnik rendering engine, a code editor, and a data inspector. It is available for Linux and Mac OS X. It is built by Development Seed who also offer MapBox, a paid-for hosting service for tiles created with the application.

Third-party providers

Several OpenStreetMap service providers will be happy to work with you to host the map tiles with the stylesheet you have designed. See the provider listing.