More than a dozen companies have sprouted up in recent years to sell thousands of genetic health tests, ranging from Google-backed 23andMe to Roche.

But the consumers who order the tests often face months-long waits to get an appointment with a genetics expert who can explain the results. That's because there are fewer than 5,000 genetic counselors in the United States, which falls far short of the demand. Given the lack of training programs, genetic experts predict that the supply won't reach an equilibrium until 2024.

So a group of health veterans is forming a new technology startup called Genome Medical to train genetic experts, and provide $149 video consultations to both doctors and patients.

The company was founded by Lisa Alderson and Randy Scott, former executives from Invitae, a company that is aiming to become the "Amazon for genetics," and Harvard Medical School geneticist Robert Green.

In an exclusive interview with CNBC, Alderson said the company has raised more than $12 million from Canaan Partners, Illumina Ventures, and others.

Recent studies have found that genetic testing costs patients and their insurers between $300 million and $600 million each year in the U.S. alone. The market for precision medicine, which involves a boost in human genetic testing, is expected to reach $87.79 billion by 2023.

Alderson said genetic-testing companies are increasingly willing to pay for access to experts, who can help patients understand their results. The initial areas of focus for the company include reproductive health, cancer and preventative medicine.

Illumina, maker of DNA sequencing machines, is partnering up with Genome Medical for its program, known as Understand Your Genome, which offers whole genome sequencing to professionals for $2,900.

Illumina's vice president of applied genomics Dawn Barry said that Genome Medical's experts will help consumers determine if they need the test at all and what to expect. Barry described the technology as a "critical connection."

Federal regulators have expressed concern about companies that offer genetic information to consumers, without expert oversight. The U.S. Food and Drug Administration made that clear in November of 2013 when it ordered direct-to-consumer testing company 23andMe to stop selling its tests, although the FDA more recently approved 23andMe tests for some specific functions. (23andMe is not a partner of Genome Medical.)

"There will be a tremendous increase and interest in utilizing genetic testing," added Genome Medical's Green. "But everyone agrees that the current medical workforce isn't prepared for that."