An estimated 850 people were set to be moved into temporary heated tents at Lipa migrant camp by Saturday evening.
"The authorities have taken charge, which is a really good thing, and are now in charge of running these new temporary locations," Peter Van der Auweraert, the UN's Western Balkans Coordinator told Euronews.
"The key issue is that the government has finally started to work on connecting the site to the electricity grid," Van der Auweraert, who is currently in Lipa, said.
He added that this paved the way for the permanent structures that are being planned for at Lipa to be "properly heated" with "proper hot water for showers and water for toilets".
A fire all but destroyed the Lipa refugee camp in the northwest of the country last month.
The Bosnian military started setting up tents on Friday for hundreds of migrants who have been stuck at the fire-ravaged camp that has no facilities to fend off freezing winter weather.
Van der Auweraert said that heavy snowfall prevented the tents from being finished on Friday, but the floors were fitted and heaters connected to generators in the last tents on Saturday afternoon.
"Of course, there is always the risk that you will have 50 or 100 people that will emerge late at night because they have heard that there are tents in Lipa," he added.
He added that he hoped plans would be approved for a permanent development at Lipa next week so that the project could be started in the coming days.
There are still around 1,500 people living around the burnt-out camp in squats, abandoned buildings and nearby forest camps, for whom "there is no immediate solution," Van der Auweraert said.
Bosnia has been criticised internationally by politicians for leaving the migrants without shelter or heating during the freezing cold weather.
Migrants did what they could to keep warm on Friday after they were caught up in a blizzard while authorities scrambled to finish setting the military tents meant to accommodate them.
"It is much too cold here," said one migrant from Pakistan. "We have too much trouble here in Lipa camp."
"Please stand with us and help us, we are in very, very, very bad condition," added another, also from Pakistan.
The UN has warned that thousands of refugees and migrants urgently need proper shelter in Bosnia after weeks outside in freezing conditions.
The organisation had said around 2,500 people were in unheated tents or sleeping rough near the northern town of Bihac where local authorities have refused to reopen a nearby reception centre.
Many were forced to return to the burnt-out Lipa camp.
Bosnia has struggled with the influx of thousands of people fleeing war and poverty in their countries in the Middle East, Africa, and Asia.
Migrants mostly flock to Bosnia's northwestern corner, which borders European Union member Croatia, from where they hope to move toward wealthier European countries. But many have reported violent pushbacks by Croatian border forces as well as hostility from Bosnian residents.