With other legal challenges under way in Britain, the outcome will be closely monitored by politicians and financial markets.
Ciaran O'Hare, a lawyer representing veteran victims' rights campaigner Raymond McCord - one of a diverse group of individuals in the case - said the judge would give his ruling at 0900 GMT (1430 IST) tomorrow, after three days of hearings earlier this month.
"We are delighted at such a quick turnaround but time is obviously of the essence," O'Hare said.
"Both sides will likely appeal to the Supreme Court but the ruling in Belfast is important because it would have to be taken into account," he said.
The campaigners argue Brexit cannot be imposed on Northern Ireland because the 1998 Good Friday Agreement, an international treaty involving the neighbouring Republic of Ireland, gives Northern Ireland residents control over future constitutional change.
"The historical context is vital in our case: we believe the Good Friday Agreement gives us a veto," O'Hare said.
McCord has joined a cross-party group of politicians and community activists taking the case, warning that the loss of EU funds could undermine the Northern Irish peace process, which is underpinned by the Good Friday Agreement.
"The EU has pledged funding until at least 2020 but the British government has given no undertaking it will continue to fund projects to bring the two communities together," he told AFP at an earlier hearing.
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