The deal followed the lifting of martial law at midnight on Friday, after Guinea's parliament refused a request from Conte to extend a state of emergency enforced by the armed forces to prevent street protests.
Sources involved in the negotiations said Conte, a reclusive diabetic in his 70s who opponents say is unfit to rule, would announce his choice of premier from the list by March 2.
The strike triggered violent clashes with security forces across the country, killing more than 120 people since it first began in January, most of them unarmed civilians.
The industrial action was initially suspended after Conte agreed to name a consensus prime minister but the unions resumed their strike on February 12 after the president broke the deal and promoted a close ally, Eugene Camara, to be premier.
Under the new deal, Camara will now be replaced.