It’s a safe bet health savings accounts are becoming a fixture in employer health benefits. Just take a look at the numbers.

In 2006, total HSA assets were $1.7 billion. By 2015, assets are expected to balloon to $29.7 billion, according to the Year-End 2013 Devenir HSA Research Report.

The investment portion of the accounts, which made up $100 million or 7% of total HSA assets in 2006, is expected to reach $3.8 billion, or 13% of HSA account assets by next year.

Asset growth in HSAs in 2014 alone is projected to increase 29.4%, according to the Devenir report.

HSAs are “here to stay and it’s obvious,” said Eric Remjeske, CEO and cofounder of Devenir Group L.L.C., a Minneapolis-based investment advisor and consultant to the HSA industry.

Parallel to the growth on the asset side is the rise on the employee enrollment side. In March 2005, a year after HSAs were introduced as a Medicare carry forward balance replacing Medical Savings Accounts, HSAs enrolled 1 million lives, according to data from America’s Health Insurance Plans.

The number of covered lives swelled to 15.5 million in 2013 and is projected to reach almost 17.5 million by the end of this year, according to AHIP.

The HSA is a unique animal, said Todd Berkley, president of HSA Consulting Services in Minnetonka, Minnesota. It is an account that straddles health care, banking and investing — industries that traditionally don’t talk to one another.

As employees and consumers connect the similarities of the HSA with those of the 401(k), with which tens of millions of workers are already familiar, the advantage of the HSA is becoming apparent, Mr. Berkley said.

Not the least of which is that health savings accounts are triple tax-free. Accounts are funded with pre-tax contributions, interest accumulates tax free and the withdrawals for qualified medical expenses are untaxed.

Also, the accounts are portable and are relatively easy to set up, and they come in different varieties. Some offer a deposit account only with minimal fees. Other HSAs offer investment accounts with dozens of mutual fund investment options and higher fees.

In recent years, larger companies — traditionally slower to adopt changes — have given HSAs their seal of approval. In March 2005, the number of HSA-covered lives in the large employer group market was 162,000, slightly above the 147,000 covered lives in the small employer group market, according to AHIP statistics.

Fast forward to January 2013 and the number of covered lives in the large group market had ballooned to 9.5 million, far ahead of the 2.5 million covered lives in the small group market, AHIP data show.

The march of the HSA is reminiscent of the growth of the 401(k) retirement savings account, Mr. Remjeske said. After employees got used to the idea of the 401(k), the concept took off. Mr. Remjeske sees no reason the same trend should not take place among HSAs, if it hasn’t already.

With cost control as the emphasis of health care reform, that has encouraged group markets to adopt HSAs. And with the Affordable Care Act’s excise tax taking effect in 2018, even more employers are considering offering HSAs, said William Applegate, vice president of Fidelity Investments.

The tax will be imposed if the total employee and employer shares of the annual health care plan premium, without dental and vision coverage, exceeds $10,200 for individual coverage and $27,500 for family coverage. The tax will be levied at a rate of 40% of the amount of the premium that exceeds those thresholds.

“For employers seeking to avoid the excise tax and to avoid paying 40% incremental costs in the form of a penalty, that’s driving a movement toward the HSA-qualified plan which can come in under the tax threshold,” Mr. Applegate said.