We don't know. James Cameron never wrote a back-story for them.
The shortest answer is that there's no canon explanation for their origin. The writer; James Cameron never created a back-story for the xenomorphs, content that each movie should stand on its own merits as this interview shows;
"Daniel Line asks more questions about the derelict which, as a writer,
I could provide plausible answers for, but they're no more valid than
anyone else's. Clearly, the dental patient was a sole crew member on a
one-man ship. Perhaps his homeworld did know of his demise, but felt
it was pointless to rescue a doomed person. Perhaps he was a volunteer
or a draftee on the hazardous mission of bio-isolating these
organisms. Perhaps he was a military pilot, delivering the alien eggs
as a bio-weapon in some ancient interstellar war humans know nothing
of, and got infected inadvertently."
If you want to go into more depth, there is an extensive speculative commentary on Aliens Wikia regarding the origin of the "xenomorph" aliens that Ripley and others encounter in the Aliens Franchise movies.
In brief, there's no in-universe description of where they came from, nor have we seen either their genesis as a biological weapon, or as a naturally evolved species on their own planet.
We do know from the film Alien that they weren't native to LV-426 and in the film Prometheus we see them being experimented on genetically (which definitely lends credence to the suggestion that the alien pilots seen in Alien and Prometheus were intending to use them as a bio-weapon) but that's about it.
There's also no indication whatsoever that the Predators had any hand in their creation.