The 23-year-old hit-man was the Railwaymen's top goalscorer last season with 27 goals but Gradi slapped him on the transfer list after he rejected a new deal at Gresty Road earlier this month.
The Crewe-born marksman was one of ten players that The Bluebirds identified as a potential summer target last week.
Talks over the weekend lead to an agreement between both clubs for Hulse, who also attracted the interest of Premiership duo Everton and Leicester City.
The striker will now have to agree personal terms and pass a medical with the Ninian Park outfit in order for the transfer to be completed.
