Under the legislation, Floridians must submit urine, blood or hair samples for testing before they can receive cash benefits from the state, The St. Petersburg (Fla.) Times reported Wednesday.
"The goal of this is to make sure we don't waste taxpayer money," Scott said in signing the measure. "And hopefully more people will focus on not using illegal drugs."
The American Civil Liberties Union of Florida has said it is considering filing suit against the new law.
The ACLU's Florida director, Howard Simon, said the measure treats people who have lost their jobs like suspected criminals.
The Florida Department of Children and Families said the law calls for some 4,400 drug tests a month.
The cost of the tests will be covered by the state if the results are negative.