Mark Karpeles, who has not been seen in public for several days, re-emerged to tell a press conference that his firm's digital vaults had been almost completely emptied.
"We have lost Bitcoins due to weaknesses in the system," French-born Karpeles said in Japanese.
"We are really sorry for causing trouble to all the people concerned," he said, before bowing deeply.
The company's lawyer said 750,000 Bitcoins belonging to customers had gone, along with MtGox's own store of the currency, which she said was around 100,000 units.
That number of Bitcoins would be worth around USD 477 million dollars, calculated against the price on the Coindesk exchange at 1030 GMT.
Karpeles said MtGox had liabilities of 6.5 billion yen (USD 64 million) and that around a million users had been affected when hackers broke into the exchange in early February.
The global virtual currency community was shaken this week by the shuttering of MtGox, which had frozen withdrawals earlier this month because of what the firm said was a bug in the software underpinning Bitcoin that allowed hackers to pilfer them.
Supporters rallied round, insisting that the Bitcoin itself is sound and the problems lay with MtGox, which they said was badly-managed and unable to cope with the burgeoning popularity of the young currency.
Kolin Burges, an investor who has kept vigil outside the Tokyo offices of MtGox for several weeks, said on Twitter on today that he would be packing up.
"Karpeles in Tokyo says MtGox is bankrupt. 750,000 customer bitcoins stolen & 120,000 company bitcoins stolen. None left #mtgox#mtgoxprotest" he tweeted.
He later added: "Packed up #mtgoxprotest for the last time and did leaving interview with Asahi TV. It's been a wild ride!"
The admission that such a huge amount of the crypto-currency has disappeared could add to calls for regulation of an industry that has taken regulators and bankers by surprise.