If you have already grown basil successfully in hydroponics, why do you still want to transfer it to soil? I guess the reason why your basil plants wilted is because of the shock that they experienced from being transferred from one medium to another. I am not sure if this could help but I think you should just move them back to water. Best of luck :)

Hello rosespurple,
I agree that trying different methods in growing plants is a nice thing, but don't forget that when you do it, you also risk the health of your plants.

Here is a link that might be useful: Hydroponics Growing: Switch a plant from hydroponics to dirt?

It wilted due to stress. Maybe a lack of water. I'm guessing there were few root hairs on the roots. Transferring from a system where roots are constantly wet to one where they are only slightly damp can be a shock. Try watering heavily. They might pull out of it. Sometimes a plant can look like it's dead when it's in shock, but pulls out just fine. But, sometimes they really are dead.

I grow all plants hydroponically at the beginning. All my soil garden plants are started in an ebb and flow system. However, these plants are in coco coir and develop some really nice root hairs. My plants rarely experience transplant shock and when they do, it's because I did something clutzy like dropped them when pulling them out. I've transplanted from DWC (where the roots just dangle in water) to soil, too. The plants suffered for a day, but pulled out of it. I thought they would die. Something to consider is that if you plant in direct sunlight, that could hurt them, too. It's best to transplant to soil on overcast days or shade the plants with something.

I'm guessing the basil is of pretty good size, too. It's best to harvest some of the leaves to reduce transpiration if the plant is used to constantly being immersed in water. I wouldn't do it now as the plants seem to be overly stressed, but in the future you might keep that in mind.

If plants have transformed their root system to "water roots", due to the fact that roots were completely submerged in water, there is absence of tiny root hairs that actually steer growth direction towards water and nutrients.

Plants that have developed and transformed their root system to "water roots" usually will not survive the move to soil or some "dry" soil-like medium or any mix. Some more hardy and mature plants may have better chances to survive the transitory process - but seedlings or younger plants will unfortunately mostly die.

Plants grown in more fibrous medium, either feed by E/F or a dripping system, keep some (or more) air roots and can (more easily) be transplanted to soil.