Greece is in negotiations with the European Union (EU) and International Monetary Fund (IMF) for as much as 86 billion euros (US$94 billion) in fresh loans to stave off financial ruin and economic collapse.
Tsipras said the new deal would be agreed soon after August 15; Hollande said by the end of the month. The two men were speaking in Egypt on the sidelines of a ceremony to inaugurate the New Suez Canal.
It will be Greece's third bailout since its financial troubles became evident more than five years ago. Negotiations in the past have been heated, but all sides are reporting progress this time around.
An accord must be settled - or a bridge loan agreed - by August 20, when a 3.5 billion euro debt payment to the European Central Bank falls due.
In a statement, Tsipras's office in Athens said he and Hollande had agreed that the deal "should and could be concluded right after August 15".
That would give enough time for the Greek parliament to approve it to enable the August 20 repayment to the ECB.
"They also agreed that everything should be done for the Greek economy to rebound, especially after the effects of the banking crisis," the statement said.
Greece's banks are in need of recapitalization by 10 billion to 25 billion euros, according to the EU.
France has been generally supportive of Greek requests for aid, contrasting with a harder line taken by Germany which has demanded stringent reform and austerity measures from Athens.
A European Commission spokeswoman said earlier in Brussels that talks with Greece on a third bailout were moving ahead "in a satisfactory way" and reaching an agreement was possible before August 20.