Syrian opposition National Coalition has chosen Ghassan Hitto as the prime minister to head a government for rebel-held regions.
Ghassan Hitto is a Damascus-born IT expert who spent decades in the US. He was elected at a meeting of coalition leaders in Istanbul in Turkey.
His first task will be to form a government to oversee services in areas captured from government forces.
Meanwhile, the US and France denounced a Syrian airstrike on the Lebanese border as a “violation of sovereignty”.
Reports from Lebanon say Syrian aircraft fired four rockets at the border between the two countries, near the Lebanese town of Arsal on Monday.
There were no casualties from the raid. Lebanese officials had earlier said it was not clear whether the rockets had landed inside Lebanese territory.
The US described the attack as a “significant escalation” of the conflict. France said the raid constituted “a new and serious violation of Lebanon’s sovereignty”.
In Monday’s vote in Istanbul, Ghassan Hitto won with 35 out of 48 votes, in what coalition leaders described as a “transparent, democratic” election.
But some senior coalition leaders are reported to have withdrawn from the vote in protest over Ghassan Hitto’s lack of military experience.
Last November, the 50-year-old moved from Texas to Turkey to help co-ordinate aid to rebel-held areas.
Earlier, the commander of the rebel Free Syrian Army said his group would work “under the umbrella” of any new government.“Any institutions not following this government would be considered to be acting illegitimately and would be prosecuted,” Gen Selim Idriss Idriss told AFP news agency.
Large swathes of northern Syria have been seized by rebels in recent months.
They are currently administered by a patchwork of local councils and armed groups who have been running some institutions, such as courts and prisons.
But reports say basic supplies such as electricity and water are limited.
Also on Monday, the US said it would not stand in the way of other countries arming Syrian rebels.
Last week saw the second anniversary of the Syrian uprising against the rule of President Bashar al-Assad, which initially began as a wave of peaceful protests but which is now often described as a civil war.
An estimated 70,000 people have been killed and more than one million people have fled Syria since the uprising began.