Mr Papandreou said German funding would not be an investment in past failures, but in future successes.
He also hailed Greece’s “superhuman” efforts to cut its debt levels.
The prime minister is in Germany for talks with German Chancellor Angela Merkel to discuss his country’s progress in cutting its budget deficit.
Mr Papandreou said the current debt crisis provided a “unique opportunity to launch important reforms that Greece badly needs to become competitive again”.
Drawing parallels with the reunification of Germany, he talked of the “rebirth of a nation”.
“Your contribution can be crucial,” he told the assembled businessmen and women.
Mr Papandreou said that in 2010 Greece had overseen the “largest fiscal consolidation in a single year [of any eurozone member]” in reducing its budget deficit by five percentage points.
Together, they will decide on whether to release the latest tranche of bailout funds the Greek government needs to pay its bills.
Ahead of the visit, Greek Finance Minister Evangelos Venizelos said that his country would receive the funds next month.
More importantly, Mr Papandreou has an eye on a key vote in Germany later this week on whether to expand the powers of the eurozone bailout fund. There is a good deal of opposition in Germany to what many people there see as underwriting the entire bloc.
European leaders are trying to agree a comprehensive package to solve the eurozone debt crisis once and for all.
However, divisions remain between member states on how best to do so.
G20 leaders met over the weekend to discuss the best way forward, but EU officials stressed that no grand plan of action had been agreed.
A number of ideas were reportedly discussed, including a 50% write-down of Greece’s government debts.
Other proposals included strengthening big European banks that could be hit by any defaults on national debt obligations, and boosting the size of the eurozone bailout fund.
However, late on Monday German Finance Minister Wolfgang Schaeuble cast doubt on plans to bolster the European Financial Stability Facility (EFSF).
“We are giving it the tools so it can work if necessary,” he said.
“Then we will use it effectively, but we do not have the intention of boosting its volume.”
On Thursday, Germany will vote on whether to approve proposals set out in July to extend the powers of the EFSF that would allow it to buy the bonds of highly-indebted countries, and to make credit available to both governments and under-capitalised banks.
Despite Mr Schaeuble’s comments, European and Asian shares rallied strongly on hopes that leaders were finally poised to act decisively.
Germany’s Dax index, France’s Cac 40 and the UK’s FTSE 100 were all up between 2% and 3% in early trading.
Japan’s Nikkei index closed up 2.8%, Hong Kong’s Hang Seng rose 4.2% and South Korea’s Kospi climbed 5%.
However, analysts warned the gains could be short lived.
“We’ve experienced these types of temporary rebounds many times before, with markets coming up for air after days of brutal selling,” said Kazuhiro Takahashi at Daiwa Securities.
“Again, this will likely be a short break before we see more evidence of progress in the Greek debt crisis,” he said.
Markets have been extremely volatile in recent weeks as investors worry that the debt crisis may spiral out of control. They have been critical of policymakers’ inability to take decisive action thus far.
On Monday, President Barack Obama also warned of the far-reaching impact of the crisis.
“[Europe] never fully dealt with all the challenges that their banking system faced… So they’re now going through a financial crisis that is scaring the world,” he said.
“It’s now being compounded by what’s happening in Greece.”