The Republican-sponsored bill, which was passed by the state Senate earlier this month, was introduced amid national concerns about the efficacy of lethal injections.
"Those who voiced opposition to this bill are primarily arguing against capital punishment in general and that decision has already been made in our state," Marty Carpenter, spokesman for the Republican governor, said in a statement.
Carpenter said the state preferred to use its primary method of lethal injection when a death penalty is issued.
"However, when a jury makes the decision and a judge signs a death warrant, enforcing that lawful decision is the obligation of the executive branch," he said.
The new law says a firing squad should be used if the state cannot lawfully obtain the substance or substances needed "to conduct an execution by lethal intravenous injection 30 or more days" before the date set for the procedure.
Several U.S. states have had to search for new drugs for their lethal injection cocktails after many pharmaceutical companies, mostly in Europe, imposed sales bans about four years ago because they objected to having medications made for other purposes being used in executions.