There's no more a fixed way of dealing with this in Latin than there is in English and, just as in English, much can be implied by your choice.
For example, you might say 'I'm a Londoner', or 'I'm from London'. The first case carries a certain nuance, that of being 'born and bred' in London itself, and in the proper context might indicate pride in the fact; the second is less definite, perhaps (but not necessarily) a shorthand for something like 'I live in (Greater) London'. Each expression is quite proper, and each might also be expressed as 'I come from London'. And you might also say 'I was born in London', 'I was born a Londoner', 'I was raised in London', or 'I live in London' — and so on.
Latin has two principal ways of forming place-related adjectives, using the endings -anus and -ensis. There's no hard-and-fast rule on which to use : though I have come across various attempts to be definite about it, I think it best to use whichever sounds best to the ear, or whichever appears more suitable to the circumstances. Sometimes, however, there is an established form : we are all familiar with romanus and possibly neapolitanus, but I've never seen romensis or neapolitensis. Equally we see hispaniensis but seldom hispanianus, though I doubt that it's possible to insist on a general rule -anus for towns and -ensis for cities.
If you want a different way of expressing yourself, then just as in English we have 'I was born in Rome', in Latin there is Romae natus sum; note that this differs from romanus natus sum ('I was born a Roman'), as does similarly the proud boast civis romanus sum of someone claiming the full rights of a Roman citizen (as did St. Paul, who most certainly wasn't from Rome). If you were a visitor to Rome from Marseille, you might claim not massiliensis sum but Massiliae ortus sum, 'I originate from Marseille'.
[Finally, you may notice some difficulties stemming from the endings of the original town-names, as in Joonas's answer with the comments in reference to Londinium. I think that both Londin(i)ensis and Londinianus, insofar as the intended meaning is clear, are acceptable. Neither, if seen in an authentic Latin text, would cause an eyebrow to be raised, while either might be selected at discretion for a translation into Latin.]