The new prime minister will have more power than his predecessors and will head the government - a role undertaken by the president since independence from France in 1958.
Camara, 64, is a senior civil servant who rose through the ranks of the Guinean administration, and is seen as close to Conte.
Boubacar Biro Barry, one of the unions' main negotiators, declined to say whether the strike order would immediately be lifted, saying union leaders would meet to discuss the announcement on Saturday.
"I have no comment to make ahead of tomorrow's meeting," he said.
Eleven people were injured earlier on Friday in the north of the country during protests calling for Conte to step down.
The protesters set up barricades on the streets, set fire to two police stations and freed prisoners in Duinguiraye, 400 km northeast of the capital, Conakry.
The strike led to food shortages and triggered violent protests against Conte's 23-year rule in towns across the former French colony.
Strike leaders had not specified who they wanted to be prime minister, but said the candidate had to be free from the allegations of corruption that have tainted Conte's recent administrations.
Mamadou Ba, one of Guinea's main opposition leaders, dismissed the nomination of Camara, a senior member of the ruling party, as an empty gesture.
"This is a provocation, and as from Monday we will demonstrate," he said.