Gov. John Carney, a Democrat, is expected to sign it.
"The Governor supports a $15 minimum wage and looks forward to a bill getting to his desk," Carney spokesman Jonathan Starkey said, according to the News Journal of Wilmington.
The Democratic-led state House approved the bill 26-15, with no votes from Republicans, the newspaper reported.
Republicans had proposed six amendments, including one that would allow small businesses to pay 85% of the minimum wage, that were defeated by Democrats.
Democrats also rejected a proposal by one of their own party members, state Rep. Sherae’a Moore, to delay each of the annual wage increases for one year for businesses employing 20 or fewer workers.
The bill has been a legislative priority for newly-elected progressives in the state.
The state’s current minimum wage is $9.25, which the bill will increase incrementally by a little more than a dollar a year until it reaches $15.
State Rep. Bryan Shupe, a Republican, proposed amendments that would have required studies of the fiscal and economic effects of the wage increases. Democrats defeated the amendments.
"The dialogue ... has not been about empirical evidence, has not been about statistics, has not been about projections and analysis," Shupe argued.
State Republicans warned that raising the minimum wage could force small businesses to shut down, higher prices on goods and services and some low-wage workers could lose more in state assistance for expenses such as rent and child care than they will gain in income.
"This is the wrong time," state Rep. Ron Gray, a Republican, said, speaking of how small businesses have suffered during the pandemic, according to the News Journal.
But Democrats contended that employees also struggled as the economy was forced to close.
It will cost the state $3.7 million per year by 2024 to raise the wage for the lowest-paid public employees, a finical analysis found, according to the newspaper.
The current federal minimum wage is $7.25.
Congressional Democrats failed earlier this year to squeeze a minimum wage increase into Biden's $1.9 trillion coronavirus relief package, which the president signed in March.
The Associated Press contributed to this report.