The demand, made by a US judge, follows an intellectual property battle the firms fought in court.
The judge said he was "concerned" that financial relationships may have influenced analysis published in newspapers and on the net.
He added the information would be useful to an appeal hearing.
The two firms have been given until 17 August to provide the information.
Oracle - the developer of the Java programming language - had pursued a patent and copyright challenge alleging it was owed about $1bn (£640m) in compensation for Google's use of its technologies in the Android system.
But the jury ruled that the patents involved had not been breached, while a judge dismissed the key copyright claim - a decision against which Oracle said it would "vigorously appeal".
Regarding the latest development Oracle said it "always disclosed all of its financial relationships in this matter, and it is time for Google to do the same".
Google said it would comply with the order.
Several instances of the firms paying commentators are already known.
Florian Mueller, a patent consultant based in Germany, revealed on 18 April that Oracle had "very recently become a consulting client" - two days after the court case began.
He had written about the lawsuit over previous months on his influential Foss Patents blog and continued to do so after his declaration, often making comments sympathetic to Oracle's claims.
When questioned by the BBC he said he could provide only a limited amount of detail about the relationship.
"There was never any request to say please do this or that," he said.
"We agreed I would still express my views and pick my topics. I wrote all the blog posts independently, and they did not see draft posts."
Google is also known to have given money to the Electronic Frontier Foundation.
The San Francisco-based campaign group posted articles including "Oracle v Google shows the folly of US software patent law" during the case.
The search giant paid $1m to the organisation in 2011 after being fined over privacy-rights violations which the EFF had championed.
Google had been given a choice about whom it should pay compensation to, since if it had shared out the cash among its users the sums paid out would have been less than the cost of distributing them.
Fortune Magazine has also reported that the Android developer had also given the EFF smaller voluntary donations in 2010 and 2011.
It is not clear what both parties will count as qualifying as payments.
Santa Clara University professor Eric Goldman told Reuters he might appear on Google's declaration list because he has written about the case while featuring Google-distributed adverts on his site.
Tim Luckhurst, professor of journalism at the University of Kent, said the case flagged up a wider concern he had about the way some writers operated.
"One of the key aspects that this highlights is the crucial difference between bloggers and professional journalists," he said.
"Journalists are professionals who understand their obligation to their listeners and viewers - not the interested parties about which they are writing. Many bloggers ignore that distinction."
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