By Andy Pasztor

U.S. air-safety regulators are set to begin key flight tests of Boeing Co.'s 737 MAX as early as Monday, with the aim of returning the planes to service around the end of the year, according to a person familiar with the details.

The airborne checks, slated to be conducted in conjunction with Boeing and scheduled to last three days, mark a long awaited milestone for getting the MAX fleet back in the air. The planes have been grounded for 15 months following two accidents that killed 346 people and dealt the biggest blow to the plane maker's reputation in its 103-year history.

The crashes, which occurred less than five months apart in late 2018 and early 2019, kicked off debates in Congress and throughout the industry about Federal Aviation Administration procedures and safeguards for approving the safety of new jetliner designs. The deaths also prompted substantial changes in decades-old assumptions about how typical pilots interact with complex cockpit automation.

A Boeing spokesman said, "We continue to work diligently on safely returning the MAX to service."

The FAA gave the green light late Friday for such flights to start as early as Monday, according to the person familiar with the details.

FAA officials have consistently said they wouldn't move toward certifying test flights or other action to recertify the MAX until all the agency's questions and concerns were answered satisfactorily.

Before scheduling test pilots to vet various software fixes and changes to the jet's flight-control systems, the FAA formally signed off on a series of Boeing technical analyses and risk assessments that had taken months. Within days of the second crash, Boeing launched an effort to develop initial software revisions to an automated flight-control system called MCAS, which misfired, overpowered pilot commands and put both MAX jets into nosedives.

Under prodding from the FAA and international regulators, Boeing since then has revised several other features of the MAX's flight-control computers and associated hardware, including agreeing to relocate certain electrical wiring under the cabin to avoid hazardous short circuits.

The test flights, once planned for the summer of 2019, continued to be postponed as FAA and Boeing experts expanded their work to cover an array of new safety issues and previously unexamined computer shortcomings.

Even if the flight tests go well, the MAX faces months of additional regulatory scrutiny-- including more testing of the plane's handling by a group of international pilots, further analyses by pilot-training officials, verification by outside safety experts and extensive maintenance work--before the jetliners are ready to fly passengers.

In addition, Canadian and European regulators are pushing for other software changes that could be phased in over a year or more, once the planes return to service.

Over the months leading up to Friday's decision, industry and government officials projected that the FAA was likely to officially lift its order grounding the planes by early fall. Airline officials have said they anticipate needing roughly two months after such a move to prepare aircraft for flight, phase them into their fleets and arrange for pilots to complete extra training in ground-based flight simulators expected to be required by the FAA. With some potentially important exceptions, international regulators are expected to follow the FAA's lead and clear the planes to fly within weeks of a final U.S. announcement.

Some 800 MAX planes are grounded, with roughly half of them in storage under Boeing's control because they were never delivered to customers.

With thousands of jetliners of various types sitting idle around the world because of the coronavirus pandemic, industry officials expect most airlines to move slowly to fit 737 MAX planes into truncated schedules.

Results of the test flights aren't likely to be released immediately, and a formal write-up could take weeks, according to industry and government officials. Later this summer, House and Senate leaders are expected to engage on provisions in rival bills intended to overhaul FAA certification of new aircraft designs.

FAA chief Steve Dickson, a former military and airline pilot, has said that before the agency's decision, he would personally test the revised software.

To boost passenger confidence in the redone flight controls, U.S. airline officials previously raised the possibility of conducting their own demonstration flights of MAX aircraft with executives and pilot-union leaders on board. The FAA has also considered strategies to explain the changes to regulators in other countries to ensure a coordinated return of the fleet.

Andrew Tangel contributed to this article.

Write to Andy Pasztor at andy.pasztor@wsj.com