Katumbi, a powerful businessman and ex-governor of the mineral-rich Katanga province, said he was "confident" after filing the complaint with the UN Human Rights Committee.
The prominent government critic told AFP he turned to the UN because the judiciary in his country had been "manipulated" by the state.
"Justice was denied us inside the country, so we were forced to turn to the international community," said his lawyer, Eric Dupond-Moretti, explaining that "we believe the (Congolese) state has violated his fundamental rights."
It maintains that he has been forced into exile in a bid to "keep (him) away from the presidential elections."
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Katumbi is a former Kabila ally who broke with the ruling party in September 2015, and a year later was named as a presidential candidate by the G7 group of opposition parties.
But Kabila failed to step down at the end of his mandate last December, sparking tensions across the vast mineral-rich nation of 71 million people.
Authorities have ordered him arrested if he returns from abroad.
Fellow opposition politician Jean-Claude Muyambo was meanwhile sentenced to five years on fraud charges linked to the same building.
DRC's influential Catholic bishops have described the two trials as "a farce".
The bishops issued the report in March as part of a New Year's Eve deal brokered by the Church to end the political crisis and pave a way for elections by the end of this year.
Since the unrest began it has claimed more than 400 lives and forced more than 1.2 million people from their homes, UN figures show.
The UN Human Rights Committee, which oversees countries' adherence to the International Covenant on Civil and Political Rights, registers around 200 new complaints each year.
It usually takes the Geneva-based committee of independent experts around three years to deliver decisions.
It does not have the power to impose sanctions.