The baby, named Brenda, is the first primate born using an egg taken not from a working ovary but from parts of the ovary implanted elsewhere in the mother's body.
This tissue contains cells that can develop into eggs, without needing a full ovary.
The egg was then removed, fertilised and the embryo was transplanted into a surrogate mother.
"This breakthrough may be a major step in preserving fertility for young cancer survivors," said David Lee, a fertility expert at Oregon Health & Science University (OHSU) in Portland, who worked on the primate project.
"In the future this procedure could allow a significant number of these cancer survivors to conceive and have healthy children," he added.
Although cancer treatments such as chemotherapy, radiotherapy and radical surgery save the lives of patients, they can damage or destroy their fertility.
The scientists restored fertility in seven monkeys whose ovaries had earlier been removed, by implanting fresh tissue from their ovaries under the skin of their arm, abdomen or kidney or in a combination of areas to determine the best site.
Six to 12 months later the scientists retrieved eggs from the monkeys, fertilised them with sperm and implanted a dozen embyros into surrogate monkey mothers, according to the research published in the science journal Nature.
"This breakthrough may be a major step in preserving fertility for young cancer survivors. In the future this procedure could allow a significant number of these cancer survivors to conceive and have healthy children"
Oregon Health & Science University
One pregnancy was established and five months later, the normal gestation period for monkeys, Brenda was born from the womb of the surrogate mother.
Earlier this week a separate research team said it had made a human embryo in a similar process, using frozen ovarian tissue taken from a cancer patient six years earlier and planted under her skin. But that experiment did not lead to a live birth.
Until now only live sheep and rodents had been born through such egg transplants.
The knowledge gleaned from the primate research brings scientists a step closer to producing the same results in humans.
"If it works in rhesus monkeys and we know that we can recover and fertilise eggs from patients, it is reasonable to believe that eventually we will be able to establish pregnancies in patients as well," Dr Don Wolf, of Oregon National Primate Research Center, said.
He said the next step was try to get the same success using frozen ovarian tissue from monkeys, rather than fresh tissue as this time.
Human fertility treatments for cancer patients would depend on making the technology work with frozen tissue.
"This provides cancer patients with some hope for the future," said Wolf. "This technology is developing at a significant and measurable rate and there is promise that at the end it technology will work."