Mozilla will not learn whether it has broken the record for another week or so while Guinness World Records officials pore over download logs and verify the attempt.
The promotion got off to a shaky start on Tuesday morning when initial demand pushed Mozilla's servers offline for a short period.
Mozilla managed to recover and demand for Firefox 3 had reached a peak of 14,000 downloads a minute by midday.
By mid-afternoon the traffic had slowed, and Mozilla executives placed the estimate at five to seven million downloads by the end of the attempt.
Traffic remained strong through the evening, however, and the total eclipsed 8.2 million as the 24-hour period drew to an end, according to Mozilla.
"It has been a very busy 24 hours for Mozilla folks around the world," said chief executive John Lilly.
"Like everything that is Mozilla, this involved people far beyond Mountain View and far beyond the borders of any one company or group."
More than a quarter of the total came from US users who downloaded some 2.6 million copies of the browser in the first 24 hours. Second was Germany with 738,000, followed by Japan with 406,000.
The UK accounted for 313,000 downloads, while France logged 306,000 and Spain 310,000.
Scandinavia, which has traditionally been a stronghold for the open source browser, turned in relatively small numbers. The three countries accounted for fewer than 180,000 downloads in total.
Other notable numbers include Iran (260,000), China (174,000) and Russia (111,000).
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