"France has reaffirmed its greatness and power, its devotion to universal human values," Armenian President Serzh Sarkisian said in a letter to his French counterpart Nicolas Sarkozy.
"This day is exceptional for all those who are struggling for the protection of human rights, for the condemnation and prevention of crimes against humanity," Sarkisian wrote.
He said it was "a historic day for Armenians all over the world", praising Sarkozy for his "personal commitment" to the bill which has infuriated France's NATO ally Turkey.
Several hundred young political activists and students gathered outside the French embassy in Yerevan to express their gratitude, bringing flowers and candles and waving French and Armenian flags.
Some carried placards with slogans such as "France is a guarantor of historical justice", while others chanted: "Long live Armenia, long live France, long live the Franco-Armenian friendship!"
"We came here to say thank you to the French ambassador and ask him to convey our huge thanks to President Sarkozy, the senators and the French people," one of the rally's organisers, Artur Kazarian, told AFP.
"France has shown once again that it places human values higher than economic and military interests," he said.
"We had faith in the president of France and this bold nation which showed that it is not afraid of Turkey," another demonstrator, Vera Martirosian, told AFP.
Armenia and its diaspora in countries around the world including France have long campaigned for international recognition of the mass killings by Ottoman Turks during World War I as genocide, despite strong denials from Turkey.
Armenian newspapers also welcomed the vote, one of them praising the French Senate for approving the bill despite Turkish warnings of a tough diplomatic reaction, under the headline "Bravo France".
"The French Senate made a step forward despite the hysterics and threats from the Turkish side," the Yerkir newspaper said.
Newspaper AZG accused Ankara of attempted "blackmail" against Paris, while Iravunk speculated approvingly that "France has shown a red light on Turkey's road to the EU".
The issue has poisoned relations for decades between the two neighbours whose mutual border remains closed, and still inspires intense feelings among Armenians, who hold a thousands-strong remembrance procession each year to the genocide memorial monument overlooking the capital.
Armenia says that planned massacres and deportations left more than 1.5 million of its people dead, but Turkey puts the number at up to 500,000, describing the bloodshed as civil strife.