MySQL has an undocumented syntax to sort nulls last. Place a minus sign (-) before the column name and switch the ASC to DESC:
SELECT * FROM tablename WHERE visible=1 ORDER BY -position DESC, id DESC
It is essentially the inverse of position DESC placing the NULL values last but otherwise the same as position ASC.
A good reference is here http://troels.arvin.dk/db/rdbms#select-order_by