The browser, codenamed Fennec, will initially be available for Nokia's N900 phone, followed by other handsets.
It is currently going through final testing and could be released before the end of the year, said Jay Sullivan at Mozilla, the group behind Firefox.
The open-source browser will be able to synchronise with the desktop version.
Software will mean that any web pages open in a user's desktop browser will automatically open in the mobile version.
"At the end of the working day you can walk away from your computer and keep on going on your phone," Mr Sullivan told the BBC.According to the Mozilla wiki mobile project page, the Fennec test build in question is currently in its fifth beta release; assuming the release candidate process moves along quickly, it could be ready by year's end. This build is designed for Nokia's Linux-based Maemo platform, which includes both the N900 and N810 series smartphones.
Where Fennec heads from here, however, is less clear.
In theory, Mozilla's work on the Nokia Maemo platform should translate well to other Linux-based smartphone operating systems. In practice, the devil is always in the details. While more adventurous are willing to experiment (and accept the occasional crash or hiccup), most smartphone users will wait until Mozilla delivers a release tailored to a specific smartphone OS.
According to Mozilla, a Windows Mobile version of Fennec is currently in alpha testing. Since WinMo is a dying smartphone platform at this point, I'm not sure why this is even a priority for their developers.
All things considered, it may be a while before most smartphone users get to try out Firefox. That's a shame, since it sounds like an interesting project. Since Fennec will employ the same add-on architecture that desktop versions of Firefox support, Mozilla's add-on developer community is sure to have a field day creating new and interesting mobile applications.
Oh, and if you use an iPhone, you're out of luck. Apple will only allow iPhone users to run browsers based on its Webkit engine, which the company uses for its own Safari browser.