It is understood Mr Story has been formally offered the vacant seat by the returning officer for the European elections in Yorkshire and intends to accept.
The decision by outgoing prime minister David Cameron to offer Lord Kirkhope a peerage has triggered a fierce internal battle over who should replace him as one if the two Conservative MEPs for Yorkshire in Brussels.
European elections are fought on a regional list system where parties earn seats depending in their share if the vote.
If a sitting MEP later resigns the seat normally goes to the next person on the list at the last election s.
In 2014, Mr Story was second in the Conservative list in Yorkshire but party sources have been suggesting in recent weeks he would not be allowed to take the seat with Leeds councillor John Proctor said to be in line.
However, it is understood Mr Story has recieved a letter from Tom Riordan, Leeds City Councils chief executive and the returning officer for European elections in Yorkshire, formally inviting him to become the MEP.
It is further understood Mr Story intends to defy his opponents in the party and take up the seat.