The Seasiders' attacker, fresh from scoring a brace against Goole in the Emirates FA Cup First Qualifying Round, will link up with the Northern League outfit while also remaining available to Nathan Haslam during the 2023/24 season, writes Liam Ryder.
As part of the deal, Whitby Town will have first choice if Storr is required to be a part of the match day squad.
On the deal, Nathan Haslam said: "Jos is first and foremost a Whitby Town player. This deal just gives us some flexibility for him and his immediate development.
"He's heading off to university in Newcastle so the deal makes sense and I know he's in very good hands with Nick Gray and Whitley Bay as a club.
"The same strategy worked for the development of Soni Fergus and Coleby Shepherd which has proven to bring these young players on to be regulars in our side."