As of Monday, parents will be able to ramp up on tax savings to help cover the cost of private school.

The Tax Cuts and Jobs Act has expanded the use of 529 plans – accounts that allow savers to accumulate money and pay for college on a tax-free basis – to include elementary and secondary school expenses at public, private or religious institutions.

That means individuals can take up to $10,000 in distributions annually from their 529 plans to pay for private school tuition and books through 12th grade – in addition to using their account proceeds for college costs.

"It's a great way to start saving for school, especially with the new tax bill going into law and hopefully offering larger refunds," said Jeff Fosselman, a certified public accountant and senior wealth advisor with Relative Value Partners in Northbrook, Illinois.

Individuals can also save on state and gift taxes when making contributions into the 529 plan.

Here's how to get the most out of this tax-advantaged savings account.