Hussein Salem was arrested by police in Madrid last June on suspicion of money laundering and corruption.
The court set his bail at 27m Euros ($36m; £22m), while police froze more than 32.5m Euros in cash, properties worth 10m Euros and five luxury cars.
Money was allegedly obtained illegally in Egypt and sent to accounts in Spain held by Mr Salem through several firms.
Mr Salem is reported to have left Egypt on 3 February 2011, eight days before Mr Mubarak was forced to resign by anti-government protesters.
He was charged in Egypt with fraud and financial speculation in May along with Mr Mubarak and the ex-president’s two sons, Alaa and Gamal. Their trial ended last month and a verdict is expected in June.
Mr Mubarak has been held in custody since April, but it was not until two months later that Mr Salem was detained by Spanish police along with his son, Khaled, and Ali Evsen, a Turkish businessman who is alleged to have set up the companies used to funnel money from Egypt to Spain.
They appeared the next day before two magistrates at the National Court in the Spanish capital, one handling the Spanish money-laundering investigation and the other dealing with the international arrest warrant.
The judges set bail for Mr Salem, who holds both Spanish and Egyptian passports, at 27m euros – 12m euros in the Spanish case and 15m euros in the Egyptian extradition case. Bail for Khaled Salem, who also has Spanish citizenship, was set at 6m euros and for Mr Evsen at 18m euros.
On Friday, the National Court informed the Egyptian ambassador that it had “agreed to hand Hussein Salem and his son Khaled to Egypt”, reported to BBC.
The 77-year-old businessman is alleged to have siphoned $714m in public money out of a deal to sell natural gas to Israel.
Prosecutors say Mr Mubarak allowed a company in which Mr Salem was a major shareholder to buy gas from the government at below market price, and then resold the gas to Israel at a substantial mark-up.
Mr Mubarak is also alleged to have allowed Mr Salem to buy a large amount of land on Egypt’s Red Sea coast from the government at a discounted price in return for five luxury villas.