Markell signed the bill Wednesday afternoon in Dover.
The bill was quickly approved this month by state lawmakers, who worked to enact a permanent ban on the drugs before a temporary ban imposed by state officials last year under an emergency rule expired.
Authorities say chemicals used to make bath salts can produce effects similar to those of cocaine, LSD and methamphetamine, and can lead to dangerous, violent and suicidal manner.
Authorities have reported a spate of violent incidents linked to use of such designer drugs, including the stabbing death of a New Castle county police officer.
