The group that consists of 25 men, seven women and 11 children was delivered by Ugandan authorities at Kagitumba One-Stop Border Post in Nyagatare District and received by Rwandan immigration officers.
They are part of the thousands of Rwandans who have been left at the border with Uganda after lengthy periods of detention, authorities in Kigali say.
The moves comes after Ugandan President Yoweri Museveni and his Rwandan counterpart Paul Kagame signed an MOU during a quadripartite summit in Luanda, Angola in August 2019, which was also attended by the host Angolan President Joao Lourenco and Democratic Republic of the Congo (DRC) leader Felix Tshisekedi.
The two neighboring countries recently witnessed frosty relations as they accused each other of spying, provocative border incidents which could lead to open hostility.
Rwanda has advised its citizens not to travel to Uganda where they face possible harassment, incarceration and deportation.
Rwanda say the illegal detention of its citizens in Uganda is at the heart of strained relations with Kampala whose officials have been accused of economic sabotage and backing militias attempting to bring down the government in Kigali.
Uganda has previously denied the accusations.