The bill, which passed the state Senate by a vote of 12-9 on Thursday, makes the consumption or possession of less than an ounce of marijuana in private punishable with a civil fine.
Public use would still be punishable as a misdemeanor, and could result in fines of up to $200 or imprisonment of up to five days, according to the bill.
The legislation, which Markell signed almost immediately after it cleared the legislature, is in line with similar measures that have been signed into law in California, New York and several other states.
Marijuana use is completely legal in Colorado, Washington and Alaska and it will become legal in Oregon on July 15.
Allen St. Pierre, executive director for the National Organization for the Reform of Marijuana Laws, said the governor's swift signing is emblematic of the nation's overall relaxed attitude toward recreational marijuana use.
"He didn't seem to let it sit more than five minutes on his desk," St. Pierre said. "In the 45 years we've been doing decriminalization legislation, that stuff usually festers for weeks, if not months."
The Illinois state Senate passed a similar bill in May, but it remains on the desk of Republican Gov. Bruce Rauner, whose spokesman recently said the governor is still considering his decision. St. Pierre said a victory for marijuana advocates there would be huge, given the number of marijuana arrests that take place each year in a city like Chicago.
While there are no other legalization or decriminalization bills pending in state legislatures this year, a number of ballot measures could soon push the marijuana issue to the forefront in Ohio, Michigan and California.
Michigan Democrats are attempting to push a similar ballot measure. And legalization is also expected to be put to a popular vote in California next year. Lt. Gov. Gavin Newsom has already come out in support of it.
The Delaware bill will go into effect in December.