Brewer's decision announced Wednesday means the federal government will set up an online marketplace for the state, offering subsidized private health coverage to the middle class.
Brewer, who reiterated her opposition to the health care overhaul, said there are too many costs and questions associated with a state-run exchange.
Federal requirements mean the state "would wield little actual authority over its 'state' exchange," she said in a statement.
"The federal government would maintain oversight and control over virtually every aspect of our exchange, limiting our ability to meet the unique needs of Arizonans and the Arizona insurancemarket," she said.
Brewer sent a federal official a one-page letter disclosing her decision.
Her announcement preceded a Dec. 14 deadline for states to declare whether they'd run their own exchanges.
A decision to create an exchange would have been subject to approval by the Republican-led state Legislature.
Though the Nov. 6 election results reduced the size of Republicans' majorities in the state House and Senate, a Brewer push to create a state-run exchange would have faced a fight from GOP lawmakers who oppose the law.
An alliance of hospitals, insurance companies and business groups wanted Arizona to have a state-run exchange, arguing that it would increase coverage while giving the state flexibility in designing a program to its liking.
Conservative advocacy groups such as the Goldwater Institute stand in opposition. They say Arizona shouldn't help implement a law that could foist new expenses on the state and raise health insuranceprices for residents.
Brewer's administration spent two years planning for a possible exchange, accepting approximately $31 million of federal funding to pay for the advance work.
As part of that planning, Brewer in September selected a minimum benefits package for a state-run exchange based on current insurance coverage for state employees. She noted in a Sept. 28 letter to the Obama administration that the package she chose excludes abortion coverage.
While some Republican governors in such states as Texas and Maine have balked at creating state-run exchanges, others in Nevada and New Mexico have opted to proceed.
On another implementation issue with state versus federal considerations, Brewer has decided it was better to have the state run its own program to review health insurance rates, rather than leave that to the federal government. The state has formally approved rules for a rate-review program.
Brewer still must decide whether to expand eligibility for the state's Medicaid program as called for by the law.