Once the formalities of their expulsion were concluded, the 73 adults and children boarded two trucks and left Phuket Immigration headquarters in Phuket City at 4pm.
The group included 14 females, some of them among the 16 children. There were 10 children under the age of 10, including three just three years old.
It was the first time family groups have been sighted, with thousands of oppressed Rohingya now taking to the sea in record numbers.
The decision was made last night to treat the Rohingya group as though they had landed in Thailand. They had been intercepted at sea off southern Phuket after their boat's motor ran out of fuel.
The trip to Ranong, a port on the border with Burma, will take four hours.
The group were treated with compassion by Navy officers and local police who recognised that the children especially were at risk in making such a perilous journey in an open boat.
The voyagers had taken 13 days to travel to Phuket from Buthiduang on Burma's northern coast. It was their hope to continue to travel on to Malaysia.
Their chances of being ''helped on'' were good until it was decided the children should not be placed at such great risk.
Phuketwan supplied the group with water, milk, snacks, biscuits and chocolates before they departed this afternoon.
The group was transferred from the ricketty boat, just a few hundred metres from Rawai, about 1am today.
Two large families contain all the children. Nine of them belong to two sisters, travelling with one husband and nine children.
The other family consists of a mother, a father and their seven children.
It's not known what will happen to the group once they reach Ranong. Rohingya cannot go back to Burma because they are not citizens, and not wanted there, yet some families have lived in Rakhine state for hundreds of years.
Most Rohingya sent back to Ranong end in the hands of people traffickers who organise for them to travel south again in a boat, provided they can pay a new fee. Others are forced to work to raise the money.
The reason for the tears today was because, as the leader of the group said yesterday: ''Our families put to sea because there is no hope in Burma. If we stay, we will die.''
Asean countries close to Burma - Thailand, Malaysia, Singapore and Indonesia - have opted to deal with the problem of thousands of Rohingya putting to sea rather than insisting Burma end its racist intolerance.
Thousands of Rohingya homes have been torched since so-called ''community violence'' broke out in June.
The reason why women and children are now travelling on Rohingya boats is because they no longer have homes to stay in.
At least 20,000 Rohingya are expected to have set out for sanctuary by sea before this October-April ''sailing season'' ends.