The key travel hub has been closed since two men blew themselves up in the departure hall on March 22 in coordinated blasts that also struck a metro station in the Belgian capital, killing a total of 32 people.
The departure hall was badly damaged, and a tent-like check-in facility is being used as a temporary substitute.
The attacks at the heart of Europe shocked the country and many hope the airport's reopening, even on a limited scale, will help turn the page on the traumatic events.
Brussels Airport chief executive Arnaud Feist on Saturday said the partial resumption of services would start with three "symbolic passenger flights" to the southern Portuguese city of Faro, Athens and Turin, northern Italy.
"These flights are the first hopeful sign from an airport that is standing up straight after a cowardly attack," Feist said.
Tough new checks will be in place after police threatened to go on strike if security were not improved, and travellers have been asked to arrive three hours before departure time.
One of the biggest changes will be that only passengers with tickets and ID documents will be allowed into the makeshift departure hall, and their bags will be checked before entering. Once inside, passengers will also undergo the usual security checks.
The airport will initially only be accessible by car. Vehicles will be screened and subject to spot checks, while extra police and soldiers will be on patrol throughout the airport zone.
Drew Descheemaeker, a travel agent for Thomas Cook who has a family of 11 booked on the flight, said customers appeared to be taking the new security measures in their stride.
The number of flights will be stepped up gradually, although the airport will be only be able to work at 20 percent capacity using the temporary facilities, handling 800 to 1,000 passengers an hour.
The reconstruction of the departure hall will take months.
The damage was severe, with images from the scene showing the building's glass-fronted facade in shatters, collapsed ceilings and destroyed check-in desks.
Feist said he expected the airport to start running normally again from late June or early July "before the start of the summer holidays".
The closure of Zaventem airport has wreaked havoc on the travel industry, triggering a drop in tourist arrivals and forcing thousands of passengers to be rerouted to other airports in and around Belgium.
Brussels Airport, which claims it contributes some three billion.
euros annually to the Belgian economy, has not released any figures on the economic impact of the shutdown, but top carrier Brussels Airlines