That remains to be proved, and many secular Tunisians are worried. Yet Ennahda has a unique chance to prove Islamic values can mesh with democracy at a time when reactionary Islamist forces are rising in the region. If this mix can't work in Tunisia, it won't work anywhere else in the Arab world.
The gray-haired Ghannouchi, 70, has mellowed since he founded an earlier version of Ennahda in the 1980s, when some of its members were accused of violence. He fled to exile in London after Tunisia's former ruler arrested thousands of Islamists, and became a well-known Islamic thinker who endorsed political pluralism. Jebali spent 16½ years in prison, including 10 in solitary.
Today, Jebali is the political organizer of Ennahda, and Ghannouchi the philosopher who returned home after the Tunisian revolution. "We don't see a contradiction between religion and politics," Ghannouchi says. He cites as a model the ruling party of Turkey, which endorses Islamic values but operates within a democratic system.
Ghannouchi rejects the Islamic thinking of the Taliban and also dismisses the undemocratic system in Iran, where a supreme religious leader is above institutions and above the law. "I am for the separation of religious institutions and political institutions," he says.
Both men also contend that sharia (Islamic law) is a set of principles open to interpretation - not a body of immutable demands, as Islamic hard-liners contend. "We know there are some Muslims who do not believe in democracy or freedoms in society," Jebali said. "We consider this a wrong interpretation. For us, the authority in Islam is given to the people, and even the legislative power should come from the people."
Those principles, both men say, do not rule out full rights for women. They say there is no contradiction between sharia and Tunisia's family-status law, the most liberal in the Arab world, which guarantees women equal rights with men, including the right to divorce and to have child custody. It also outlaws polygamy.
Ghannouchi says: "I've confirmed my support for the family-status law a million times and will do it again." He adds that Ennahda would seek equal salaries for men and women for the same job and would address sexual harassment in the workplace.
Still, many secular women distrust his promises. But Ghannouchi says that if his party alienates them, Ennahda will lose the next election: "More than half the voters are women, so there is no hope for anyone to win without women's votes."
Both political leaders appear to realize that they must take account of the particular characteristics of Tunisia - a Mediterranean society with close links to Europe and a high literacy rate.
"Tunisians embrace their civilization, and enjoy the good life," says Jebali. "They do not like extremes. They don't like niqab [a nearly full-face veil] or long beards, but they don't like semi-naked women."
Critics of Ennahda say the party will exert social pressure, if not legal means, to push more women to cover. And they contend that Ennahda hasn't taken a strong enough stand against the hard-line Muslim salafists who attacked a TV station for showing the animated film Persepolis, which showed a picture of God.
They also fear the Islamists can count on funding from the Arab Gulf that enables them to distribute food and cash. Ghannouchi insists, "We don't get one penny from any outside country." He points out that he has been kicked out of Saudi Arabia, denied a visa to Iran, and is under death threat from al-Qaeda.
Yes, Ennahda clearly has lots of cash, but it can't have bought all of its votes with money. In the new Middle East, many people will vote for Islamists as a reaction against political corruption, or - in Ennahda's case - because its followers are known to have suffered under past regimes.
Yet, having won a plurality of seats, Ennahda will now be judged by how it performs.
The newly elected assembly is tasked with writing a constitution, and Ghannouchi has pledged to seek consensus with secular parties. He will have to restrain followers who are more hard-line than he, and take a stronger line against salafists who use violence.
Everyone who has hoped in vain in the past for an Arab democracy to emerge should help Tunisians make their experiment work. They should also observe whether Ennahda lives up to its leaders' pledges.
"The Muslim world is thirsty for such a model," Jebali says. The rest of the world is thirsty for such a model, too.
E-mail Trudy Rubin