For many in the EU, Gul's election built on the confident return to government, last month, of the Islamist-rooted ruling Justice and Development Party (AKP), from which the former foreign minister has now resigned.
His victory, clinched Tuesday at the third attempt, has demonstrated that a former Islamist can become head of state, despite opposition from the army that believes its job is to keep Turkey secular.
The outcome has further established Ankara's democratic credentials at a time when its EU membership talks have become bogged down and made little progress since they began almost two years ago.
"This provides an opportunity to give fresh, immediate, and positive impetus to the accession process to the European Union, through progress in a number of key areas," EU Commission president Jose Manuel Barroso said Tuesday.
French President Nicolas Sarkozy's pledge this week not to hold up the talks as long as EU experts begin "reflection" soon on the extent of the growing bloc's borders, might mean more.
It could pave the way for new chapters or policy-negotiating areas - there are 35 in all - to begin, and removes, at least temporarily, the biggest obstacle to joining that Turkey faces.
"I am quite optimistic after the election of Gul and Sarkozy's speech," said Joost Lagendijk, chairman of the Turkey-EU delegation in the European Parliament.
"Turkey does not have any excuse, now, not to renew the spirit for reforms," he said.
Andrew Duff, a British liberal MEP, said: "Gul's election, and the formation of a new government have been very impressive.
"Now, gradually, the Europeanizing of Turkey will continue and, in due course, the French will be quite happy to accept Turkey as a full member of the family," he said.
But even the most optimistic analysts concede that Turkey's talks with Europe's rich club will run for at least another 15 years.
Its candidacy has long-troubled many EU member nations, concerned at trying to bring a large, mainly-Muslim, and relatively-poor country into a bloc already struggling to run smoothly with 27 members.
After opening a first policy chapter on "science and research" in June 2006, Brussels froze eight chapters due to Ankara's ongoing trade dispute with Cyprus.
It was then decided to continue discussion on chapters not linked to trade policy.
In April, the EU and Turkey began talks on "enterprise and industry policy," then in June opened "statistics" and "financial control," but decided not to begin "economic and monetary policy" amid stern opposition from France.
In all, four chapters are under way, well behind the 12 opened with Croatia, which began its membership talks on the same day in October 2005.
Katinka Barysch, analyst at the Center for European Reform in London, said that Prime Minister Recep Tayyip Erdogan has every interest in focusing his new government's attentions on deepening EU-oriented reforms.
Turkish intellectuals "remain suspicious of Gul and Erdogan and all of them, but they do give them credit for the modernization that has already taken place," she said.
"I think Erdogan and Gul ... understand that they need to continue on this."
The International Crisis Group, in a report this month, urged Erdogan "to use his new mandate to step forward with a bold further-reform program, catching Europe's imagination with some sweeping new gestures."
High on the EU's list is improving economic and justice reforms and, particularly, freedom of expression.
© 2007 Agence France-Presse
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