A Twitter account is giving a rolling score, and the number of downloads stands at 999,786,184 at the time of writing.
Although it is important to distinguish between downloads and users, the number of people adopting the browser is significant. Firefox has gradually increased its standing in the marketplace, and is firmly in second place behind Microsoft's Internet Explorer (IE).
Figures released in June by W3counter show that Firefox had about 34 per cent of the market, while Microsoft laid claim to approximately 60 per cent. Just two years ago, Microsoft's share was over 90 per cent.
Recent moves by the European Commission may cause Microsoft to lose even more of this share. Anti-competition measures could force the firm to remove IE as the default browser in Windows-based machines, and give consumers the choice of as many as 10 different browsers.
Mozilla released version 3.5 of Firefox on 30 June, logging nearly five million downloads in just 24 hours.
"So much is happening on the web right now, and it's a great time for browsers," said Mozilla chief executive John Lilly. "Firefox 3.5 brings together the most innovative web technologies, and delivers them in the most complete and powerful modern browser."
The firm was awarded a Guinness World Record after the release of Firefox 3 in June last year for the highest number of software downloads in a day, at eight million.
A web site celebrating the one billion download mark is already online, but shows only a holding page at this time.