“This transaction is centered around creating an aggressive ultralow fare competitor to serve our guests even better,” Spirit President and Chief Executive

Ted Christie

said.

The companies valued the deal at $6.6 billion, including the assumption of net debt and operating leases.

The consolidation comes as the travel industry continues to claw its way back toward pre-pandemic levels despite higher costs, labor shortages and disruptions caused by Covid-19.

Airlines that focus on offering cheap fares to leisure travelers—as both Spirit and Frontier do—have added capacity back more quickly than larger rivals that have been held back by a slower recovery in business and international travel, and have returned to ambitious growth plans. But they face additional competition from larger airlines such as

American Airlines Group Inc.

that are increasingly chasing the same pool of customers.

Upon the deal’s close, Frontier will own about 51.5% of the combined company, and its chairman,

William Franke,

will become chairman of the combined company’s board. Shares of Spirit rose 17% Monday, while Frontier stock rose nearly 3.5%.

Mr. Franke has had his eye on a combination between Spirit and Frontier for years. He was Spirit’s chairman when Frontier was up for sale in 2013, and pitched fellow Spirit directors on buying the carrier. He ended up resigning from Spirit, and Indigo Partners LLC, his private-equity firm, purchased Frontier from Republic Airways Holdings that year for $36 million in cash as well as assumed debt and leases.

Mr. Franke and

Barry Biffle,

Frontier’s CEO, transformed Frontier into an ultralow-cost competitor to Spirit. Analysts, investors and bankers have speculated about a merger between the two airlines since. Before the pandemic, in 2019, Spirit and Frontier were the seventh- and eighth-largest U.S. airlines by traffic, according to U.S. government figures.

The two airlines said together they will be able to grow more quickly than they would apart, allowing them to bring additional low-cost service to underserved routes in the U.S., Latin America and the Caribbean and to hire an additional 10,000 workers by 2026. Together they could add additional small cities like Eugene, Ore., and would be more likely to gain a foothold in places they have struggled like Jackson, Miss., the airlines said.

Still, the deal must get past regulators, who have taken an aggressive stance on antitrust enforcement under the Biden administration. The Justice Department last year filed an antitrust suit challenging a partnership between American Airlines Group and

JetBlue Airways Corp.

, describing their cooperation as a backdoor attempt to consolidate the industry and alleging that the airlines’ cooperation would suppress competition and lead to higher fares.

The Justice Department for years has been concerned about a reduction in airline competition and has been under pressure from antitrust advocates to do more to prevent it. The Obama administration initially challenged American’s merger with US Airways in 2013 but then settled the case and allowed the deal in exchange for concessions from the airlines.

In 2016, the department allowed Alaska Airlines to acquire Virgin America Inc. in a $2.6 billion deal, but required Alaska to significantly scale back a partnership with American to proceed.

Some analysts and industry observers said regulators may view a combination of two smaller carriers differently than any deal involving the largest four airlines, which account for about 80% of U.S. seat capacity, according to aviation-data provider Cirium. In its suit against the partnership between American and JetBlue, the DOJ raised concerns that the arrangement would make JetBlue less likely to pair up with another smaller airline—something it said could be more disruptive to the industry.

“While the Justice Department has been skeptical of further airline consolidation and even alliances with antitrust immunity, they’ll be hard-pressed to block this one,” said Kenneth Quinn, an attorney at Clyde & Co., who represented Frontier when it was acquired by Republic Airways in 2009. While the two airlines have some overlap, they are most often going head-to-head in leisure destinations with few barriers to entry rather than in the most congested airports, he said.

Frontier and Spirit said their networks will complement one another, with Denver-based Frontier’s strength in the western U.S. and Florida-based Spirit’s larger presence in the East. The two airlines overlap on some 519 routes—18% of their combined network—according to an analysis by Cirium.

Mr. Biffle, Frontier’s CEO, said Monday that the merger would make the bulked-up airline a more formidable competitor.

“For years, we’ve been dealing with the hegemonic domination of the Big Four in the United States. And now more than ever, we need competition in this country and that’s what this does,” Mr. Biffle said in an interview. “This provides more low fares to more people in more places.”

A Justice Department spokeswoman declined to comment.

Frontier on Monday dealt with a separate challenge, as a technology issue led to delayed and canceled flights. A ground stop was in place for Frontier’s flights for a period Monday morning as the airline addressed the problem. About 130 flights, or 25% of Frontier’s operation, were canceled, according to FlightAware, a flight-tracking service. A spokeswoman for Frontier said the problem was identified and resolved and the airline was working to restore its schedule for the rest of the day.

The combined company’s management team, branding and headquarters will be determined by a committee led by Mr. Franke before the close of the deal. The deal is expected to close in the second half of this year, pending regulatory approval.

Spirit shareholders will receive 1.9126 shares of Frontier in addition to $2.13 in cash for each share of Spirit they own, the companies said. At Frontier’s closing stock price on Friday of $12.39, that implies a value of $25.83 a share for Spirit, representing a 19% premium over the stock’s closing price on Friday.

In addition to the deal, both Spirit and Frontier also posted their latest quarterly results on Monday. Like other airlines, the two low-cost carriers said the Covid-19 Omicron variant hurt their fourth-quarter results.

Holiday travel helped U.S. airlines bring in more revenue at the end of last year than any quarter since the pandemic began to ravage travel demand in 2020. But major carriers posted losses and have said the new variant and a surge of Covid-19 cases have temporarily dimmed their prospects.

Spirit said that disruptions in December because of staffing shortages and the Omicron variant led to a hit of about $30 million to its adjusted earnings before interest, taxes, depreciation and amortization.

Write to Alison Sider at alison.sider@wsj.com and Will Feuer at will.feuer@wsj.com