Malaysia's attorney general cleared Mr Najib of allegations of corruption on Tuesday after ruling that the money was a donation from the Saudi royal family.
Mr Najib had denied that the money came from state investment fund 1MDB.
The Saudi source said the donation was made amid concern in Riyadh about the influence of the Muslim Brotherhood.
At the time, Malaysia's opposition alliance included the Pan-Malaysian Islamic Party (PAS). Its founders were inspired by the Brotherhood, although there is little evidence the Brotherhood actually has much support in Malaysia.
Mr Najib's coalition went on to win the election, but with one of its poorest showings in more than 50 years in power.
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The secretive donation to Mr Najib was allegedly paid over in several wire transfers between late March 2013 and early April 2013, just ahead of the election on 5 May.
The well-placed Saudi source, who has asked not to be named, told the BBC the payment was authorised from the very top - from Saudi Arabia's late King Abdullah - with funds coming from both his personal finances and state funds.
Prince Turki bin Abdullah, one of the king's sons, is reported to have had extensive business dealings in Malaysia.
The purpose of the donation was simple, said the Saudi source - it was to help Mr Najib and his coalition win the election, employing a strategic communications team with international experience, focusing on the province of Sarawak, and funding social programmes through party campaigning.
But why should the Saudis care about an election in a non-Arab country more than 6,000 km (3,700 miles) away? The answer, the source said, lay in their concerns over the rising power of the Muslim Brotherhood, which they consider a terrorist organisation.
The Saudis were already upset at events in Egypt, where President Mohammed Morsi was busy consolidating the Brotherhood's hold on the country.
It would be another three months before Mr Morsi was to be deposed by the army, and the Saudis were convinced that the opposition was being supported by the Brotherhood and Qatar, which backed the Brotherhood and other Islamist groups in the Middle East.
So how unusual is it for the Saudi royal family to hand over this amount of cash in a personal donation? Not at all, said the Saudi insider, adding that Jordan, Morocco, Egypt and Sudan have all been beneficiaries of multi-$100m donations from the Saudi royal purse.
"There is nothing unusual about this donation to Malaysia," he said. "It is very similar to how the Saudis operate in a number of countries."
Saudi Arabia was quick to support the overthrow of Mr Morsi in Egypt, providing the military-backed government with billions of dollars in aid and loans.
Jordan has been the beneficiary of more than $1bn in Saudi development funding, while Riyadh has deposited more than $1bn in Sudan's central bank and signed deals to finance dams on the Nile. Morocco has been provided with oil, financing, investments and jobs in recent years.
However, questions are still being asked about the secretive and convoluted nature of the money transfer, and the fact that Malaysia's prime minister returned 91% of it just four months later. The remaining $61m has not been accounted for.
A British corporate investigator with extensive experience of the Middle East told the BBC that the $681m was paid through the Singapore branch of a Swiss bank owned by the rulers of Abu Dhabi.
"It is very murky", he said. "This case will never be fully cleared up until the Saudis and the Malaysians release all the transaction data, and that has not happened."
There has been growing outrage in some circles in Malaysia that the attorney-general has closed the file on this case and cleared the prime minister of any offences.
Clare Rewcastle Brown, who has reported extensively on the issue for the Sarawak Report, said the claim that the payment to Mr Najib was a Saudi royal donation for political purposes needed to be treated "with considerable caution".
She told the BBC that the $681m was far more likely to be connected to money raised by 1MDB, much of which is reported to have gone missing.
The $681m (Â£479m) deposited in the bank account of Malaysian PM Najib Razak by Saudi Arabia was to help him win the 2013 elections, a Saudi source says.