Short answer. Yes. Article 696 makes every successive owner or possessor who fails or refuses to abate a nuisance started by a former owner liable in the same manner as the one who created it. Inheriting the problem is not a defence; what creates your liability is leaving it in place.
What the law says
Every successive owner or possessor of property who fails or refuses to abate a nuisance in that property started by a former owner or possessor is liable therefor in the same manner as the one who created it.
Civil Code, Article 696 — Liability Of Successive Owners. Read the full provision →
Liability attaches to your own omission
The article does not transfer the seller's liability to you; it creates a fresh one out of your own conduct. What you are answerable for is failing or refusing to abate — so the person harmed does not have to trace anything back to the person who built the thing, and you cannot answer him by naming your predecessor. The phrase in the same manner as the one who created it is what makes this bite: your position is no better than the original wrongdoer's once you have left the nuisance standing.
Possessors too, not only owners
The article reaches every successive owner or possessor, which pulls in lessees, occupants and anyone holding the property. A tenant who takes premises with a defective discharge, an unsafe structure or a source of fumes already in place is within the provision if he leaves it alone. That is worth knowing on both sides of a lease: an owner cannot assume the problem has become the tenant's alone by handing over possession, and a tenant cannot assume it stayed the owner's because he did not build it.
What actually ends the exposure
Abating it. Not disclosing it to the neighbours, not proving it predates you, not negotiating with the seller — those may sort out who ultimately pays, but they do not answer the person the nuisance is harming. The exposure runs for as long as the condition does, which is why an unresolved dispute with the seller is a poor reason to delay. Removing or correcting the condition first and recovering afterwards is almost always the cheaper order of operations, and it stops the liability from continuing to accrue.
Then look at what you were told before you bought
Your claim against the seller is a separate matter and it turns on the sale documents and what was disclosed. Keep the deed, any representations or warranties about the property's condition, the listing material and the correspondence during negotiation, together with whatever inspection was done. Date the condition itself if you can — photographs from before your purchase, or the neighbours' earlier complaints — since establishing that it was already there is the foundation of any recovery from the person who left it for you.