Based on Jurassic Park
As has been mentioned, it's likely that most of the original JP dinosaurs simply died. There are numerous ways this could have happened:
- Natural predation by larger dinosaurs
- The Lysine Contingency (explained as mitigated by lycine-rich food sources, but those may have been depleted over time)
- Predator overpopulation, leading to a collapse of the food chain
- Human action (such as the bombings described in the books)
It's also worth noting that the fact that "life found a way" to let the dinosaurs breed in the wild (with some female specimens changing to become male), there's no guarantee that that happened in sufficient quantities to create a viable population. Many species may have died off immediately, because they couldn't generate enough males or because they were eaten before their populations could reach a viable size.
Based on Jurassic World
However, it is also clear that the Jurassic World park has a much more potent, militarized infrastructure than the original Jurassic Park did. My personal expectation is that Day 1 of JW's construction featured a heavily-armed private military force landing on the island and re-capturing the surviving animals.
For example, it's been pointed out that the T-Rex has scars matching those of the one from the original park. A dinosaur outbreak can be chaos when it's unexpected and there are civilians in danger, but they are just animals after all. A well-coordinated, well-prepared force wouldn't have too much trouble tranquilizing the animals they could, and killing the ones they couldn't. Hell, a simple gas release from the air would probably be quite effective in pacifying or killing the native life, without any danger to the humans involved. From there they could sweep in, secure the animals in portable enclosures, and begin construction.
This is never specifically described, that I can recall, but it fits perfectly with the greater militarization and improved infrastructure highlighted so strongly in the new film. For example, when the Indominus Rex first escaped (before they realized how dangerous it was), they rapidly initiated pre-established protocols for dinosaur recapture, and mobilized well-equipped teams to bring it in. It's likely that these protocols were used, or even developed, during the re-taking of the island.