Zhvania's bodyguards found the 41-year-old slumped in an armchair near a gas heater at a friend's apartment, said Interior Minister Vano Merabishvili. "This is a tragic accident ... It was a gas poisoning," he said.
Zhvania was the senior figure in a trio of leaders who spearheaded a "Rose Revolution" of street protests that toppled veteran leader Eduard Shevardnadze in November 2003 and then installed the West-leaning Saakashvili in power.
The president's decision to name himself as a caretaker prime minister underscored the scarcity of suitable candidates to succeed Zhvania in the country of 5 million people.
"As president I am taking over leadership of executive power. I am ordering the government to return to work," he told a crowd outside Tbilisi's Holy Trinity cathedral where Zhvania's funeral is to be held.
"(Zhvania's death) is a huge blow for our country and personally for me as a president and as a person," a red-eyed Saakashvili earlier told ministers at an emergency meeting, many of them dressed in black, his own voice breaking with emotion.
"I have lost my closest friend, my most loyal adviser, my biggest ally."
European Union foreign policy chief Javier Solana said he was saddened by Zhvania's death. Russian President Vladimir Putin, whose relations with Georgia's leadership have often been fraught, sent his condolences.
Zhvania's body was found at 4:30 am (0130 GMT) when his guards, worried that he was not answering his mobile phone, broke down the door of the friend's apartment, said Merabishvili. The friend, a middle-ranking official, also died.