A constitutional amendment, adopted by referendum, opens the door to the Aliyev family extending its decades-long dominance of the former Soviet state - a supplier of oil and gas to the West - after Aliyev's second term ends in 2013.
The state election commission said 92.2 percent of voters backed scrapping the limit, based on results from 54 percent of polling stations. Turnout was put at 71 percent, despite an opposition call on voters to stay at home.
"These amendments are for the good of the people," teacher Sabir Farajev, 70, said after voting beneath a large photograph of Aliyev and his father. "If the president deserves to be head of state, he can be president for life," he said.
Aliyev, 47, has been president since 2003, when he succeeded his father Heydar, who led Azerbaijan first as Communist leader within the Soviet Union, then as president.
His rule has coincided with an economic boom fuelled by oil pumped to Europe from the Caspian Sea, in a region where the West and Russia are vying for influence over energy reserves.
In keeping with its location at a strategic crossroads at the threshold to Central Asia, Aliyev has tried to strike a balance between Moscow and the West, notably on energy policy.
The mainly Muslim country is key to Europe's hopes of reducing its energy dependence on Russia, a fact the opposition says has diluted Western criticism of Azeri democracy.
Rapid economic growth has brought improved infrastructure and living standards. Veteran opposition leaders are seen as weak, and fatally linked with the war and chaos that marred Azerbaijan's first years of independence - a brief spell when the Aliyevs were not at the helm.
But rights groups say Aliyev's grip on power owes more to strict curbs on democracy and to the personality cult built around his father, whose portrait and name adorn sidewalks and buildings across Azerbaijan.
(EurActiv with Reuters)