The governments were given leave to appeal but have decided against the move.
States of Jersey economic development minister Senator Alan Maclean said:
"We have been advised that the Court of Appeal would be highly likely to refer the case to the European Court of Justice. The expected timeframe for a decision would be between 18 months and two years.
"This timeframe is too long to have any material effect on local businesses and their ability to continue operations in Jersey. Therefore, the decision to appeal would be made solely on a point of principle, rather than its impact on employment in the island.
"In considering the wider implications and the inevitable uncertainty of the final outcome, it has been decided not to proceed with making an appeal. It was important that this matter was considered by the High Court given the law is, as the Judge commented, unclear in this area.
"However, the primary reason for taking the matter to Judicial Review was to save jobs. We must now concentrate all our efforts and resources in this area, rather than pursuing the legal argument any further.
"We have worked closely with our counterparts in Guernsey throughout this process, and the Guernsey Policy Council has similarly concluded that an appeal should not be lodged.
"This is a difficult time for many in the island and tomorrow (3 April) I will be meeting members of the fulfilment industry to discuss the outcome, explore ways we can support them and answer any questions they may have."