Markell signed the bill Friday morning with no fanfare.
The bill received final legislative approval Wednesday. A spokesman said Markell wanted to sign the measure as quickly as possible because of the lengthy time that will be needed to get a state-run system for distributing medical marijuana up and running.
The new law allows people 18 and older with certain serious or debilitating conditions that could be alleviated by marijuana to possess up to six ounces of the drug.
Qualifying patients would be referred to state-licensed and regulated "compassion centers," which would be located in each of Delaware's three counties and would grow, cultivate and dispense the marijuana.