Yet to make his league debut, 5'11" Oxley is capped by England at Under-18 level.
He joins the Tigers for an initial £150,000, with future payments should he prove a success.
He will be behind number 1 goalkeeper Boaz Myhill and reserves Tony Warner and Matt Duke, and Tom Woodhead signed professional terms at the end of last season.
Meanwhile, City and West Brom have both had £2million bids accepted for Bolton defender Abdoulaye Meite, and he will choose between the two clubs.