To be pedantic, if you wrote it, you own the copyright to it. You may, however, not be able to distribute your new project to anyone without a licence from the copyright owner of the work your work is derived from.
We now return you to your regularly scheduled coverage of whether or not your work is derivative:[/edit]
It depends on how much you look at the original code. At one end of the spectrum, if you slavishly translate each line of the old code into the new language, it's a derivative work, and you must comply with the licence of the original project.
On the other hand, it is possible to determine the requirements for the new project purely by examining it in use (without looking at the code). If you do that, then write the a new project from scratch which fulfils these requirements, it has nothing to do with the original project, and the copyright is entirely yours to do what you wish with. ReactOS did/is doing this with Windows.
Of course, in the real world, there is a whole spectrum of greys in between those two extremes. IANAL, but you should tend to err on the side of complying with the licence. The great thing about free software is that looking at the source code and modifying it (or re-writing it) is entirely allowed, although you still need to comply with any restrictions the licence places on derivative works.