Sharmarke and Sharif Ahmed, the Somali president who chose the new prime minister, will now attempt to bring peace to Somalia for the first time in 18 years.
In Mogadishu, the capital, several hundred people held a rally in favour of the new prime minister.
But in the southwestern town of Beled Hawo, a women's group demonstrated, saying women, plus smaller clans, had been ignored in the creation of the new government.
Sharmarke, 48, has worked with the United Nations in Sudan and Sierra Leone, holds Canadian citizenship and obtained degrees in political science and political economy from Carleton University in Ottawa.
| Sharif Ahmed, the Somali president, nominated Sharmarke as PM [AFP]
He is a member of the same Darod subclan - the Majarteen - as former president Abdullahi Yusuf Ahmed, who resigned late last year.
According to Somalia's transitional charter, the president, the prime minister and the parliament speaker are constitutionally obliged to belong to three different major clans.
Sharif Ahmed, a young cleric who was elected as president by parliament late last month, is a member of the Hawiye clan.
Professor David Shinn, an Africa expert at George Washington University, said: "I am more optimistic about the future of Somalia than I have been in a number of years.
"The selection of a PM from the large Darod clan is a wise choice to balance President Sharif Ahmed's Hawiye clan connection," he said, adding that Sharmarke's distinguished family and diaspora connections would also be advantages.
"I think this selection increases the possibility that the Sharif government will be able to pull Somalia out of its downward spiral and eventually even create an administration that is broadly accepted by Somalis."
The incoming prime minister's father, Abdirashid Ali Sharmarke, was the last democratically-elected president of the Horn of Africa country.
He was assassinated in October 1969. Days later, Mohamed Siad Barre took power in a bloodless coup and remained there until his overthrow in 1991 plunged the country into anarchy.
Sharmarke replaces Nur Hassan Hussein, who had led Somalia's transitional federal government since November 2007 and lost in the presidential election held last month in Djibouti.
According to the charter, Sharmarke will have a month from the moment of his official appointment to pick a cabinet, which will in turn have to be approved by parliament.
Mohamed Abdi Yusuf, a human rights activist in Mogadishu, said: "This is an opportunity that Somali people should benefit from because the nominated prime minister comes from a well-known political dynasty and I hope he won't miss chances to succeed peace."
"The nomination is the right choice because his father was a fair president so that I hope the son will follow him and will lead the country in the path of peace and prosperity," Amina Mohamed Issa, a resident of the capital Mogadishu, said.