Opposition in Congress had tried to block the funds but the former President pushed through the money.
State department officials said they would release the cash just hours before Donald Trump's inauguration.
The funds are to be used for political reform and governance, as well as humanitarian aid in the West Bank and Gaza, according to reports.
Holds placed by Congress are usually respected but are not legally binding.
More money was released by Mr Obama for climate change programmes, which received $4m.
Meanwhile, $1.25m was distributed to various United Nations agencies.
That cash will be spent on ozone protection and stopping sex exploitation.
The funding sent to the Palestinian Authority is likely to anger both Mr Trump and many in congress.
Congress had initially approved the fund but at least two Republican lawmakers - Ed Royce and Kay Granger - placed holds on the deal.
The block was made because the Palestinian Authority had sought membership in international organisations, it was reported.
Mr Trump's team revealed it was in the "beginning stages" of discussions to move the US embassy to Jerusalem from Tel Aviv.
The new president spoke to Israeli Prime Minister Benjamin Netanyahu at the weekend. However, officials said the embassy move was not discussed.
Mr Trump’s press secretary Sean Spicer talks were still ongoing. He said: “If it was already a decision, then we wouldn't be going through a process.”
It was also recently revealed Mr Obama's last phone call to a world leader while president was to Angela Merkel.
He used the call to praise the German Chancellor on her role in world politics while he was in office.
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