The bill was prompted by the 2012 meningitis outbreak tied to the now-shuttered New England Compounding Center in Framingham that killed at least 64 people and sickened 750 more. Inspections subsequently found unsanitary conditions at the company's facility.
Backers of the bill, including House members, say it will help protect the safety of the compounded drugs and the nation's pharmaceutical supply chain.
Currently, state pharmacy boards oversee pharmacies, including compounding pharmacies that mix customized medicines.
Under the bill, compounding pharmacies can register as outsourcing facilities and be subject to oversight by the FDA much like traditional drug manufacturers are monitored. Those that choose to remain traditional pharmacies would continue to be regulated primarily by state boards of pharmacy.
Under the new system, federal regulators would be able to track what the compounding pharmacies are making, receive reports about problems with any of the compounded drugs, and have the authority to conduct safety inspections.
The drugs make up about four billion prescriptions each year in the United States.
Deaths and injuries linked to the New England Compounding Pharmacy have been reported in 20 states, according to the federal Centers for Disease Control and Prevention.
Sen. Lamar Alexander, a Tennessee Republican, also praised the bill, saying in a statement that it would "help prevent Tennessee families from living through another nightmare like last year's tragic meningitis outbreak."
The outbreak killed 16 Tennessee residents.