Near the Centraal station, I used a service called Eelway (https://www.eelway.com/en/luggage-storage/brussels). I left my luggage there for 3 days while I was in Ghent. I think they have other locations in Brussels as they work with local shops where you can store your bags

On Brussels- Midi I saw two deferent lockers: staffed and self service. I used the self service for two cabin size suitcases and a backpack – all fit in the middle size locker, costed me 5 €.

Please note, as of 26/10/2018, all of the lockers at Brussels Central station are not working. We used a company called Nannybag. We paid online and the drop off was a tourist gift shop opposite the station on Rue Duquesnoy.
It was 6 Euro per bag.

The lockers at the airport are at level 0; you have to go outside and to the left (follow signs of lockers). I was able to stack 2 big bags and a carry on with additional laptop bag. You need to add only 1 Euro to lock (red light) and then pay when you come back. The lock is electronic and one cannot add lock of their own. The coin dispenser machine does not work and so make sure when you come back you have enough coins. The free interphone does work and you can get someone on other side. I used it for 72 hours. When you come back, scan the receipt and the display will show you the amount to be paid. Once you add required coins, the locker opens up (green light).

Train Station Facilities

At least three of Brussel’s railway stations offer left-luggage facilities. The busiest of the three stations (Centraal) is about two kilometres from each of the others and about 11 kilometres south west of Brussels airport (itself about 45 kilometres north of Charleroi airport):

Brussels North (Nord / Noord) Luggage Storage

The Belgian Rail website for Brussels North mentions automatic locker facilities:

Luggage lockers

• Automatic Luggage lockers

As of Jun 2019 automatic lockers on Noord costed €3, €3.50, €4 depending on locker size.

Brussels Central (Central / Centraal) Luggage Storage

The Belgian Rail website for Brussels Central mentions automatic locker facilities:

Luggage lockers

• Automatic Luggage lockers
• Lost property phone: 022246004

The locker sizes are:
Small, 36″x15″x12″;
Medium, 36″x24″x15″;
Jumbo, 36″x36″x20″.

For completeness sake, here is a video showing the locker facility and the signs to follow in order to get there.

Brussels South (Zuid / Midi) Luggage Storage

According to The Man in Seat 61, there is a 24h manned luggage storage office at Brussels Midi:

Brussels Midi has both luggage lockers and a staffed left luggage facility near the Eurostar check-in and Thalys reception. Both are open 24 hours a day, the staffed facility costs €4.00 per item per calendar day, the 3 sizes of lockers cost €3, €3.50, €4 per 24 hours.

This is confirmed by the Belgian Rail website:

Luggage lockers

• Staffed left-luggage service
• Automatic Luggage lockers
• Phone: 022248862

.

How Long Can You Store For?

The maximum duration for the lockers is 168 hours (7 days), after which the locker will be made empty and transferred to the staffed luggage facility. (As said here in dutch:)

HOE WERKT HET ?

Bij het gebruik van de kluizen betaal je huurgeld voor een periode van 24 uur. Na het verstrijken van deze periode, of indien de kluis tijdens de huurperiode geopend werd door de klant, moet voor een nieuwe periode van 24 uur worden
betaald. De maximale periode van gebruik is 168 uren.

Bij de betaling ontvang je een ticket dat je dient te bewaren voor de heropening van de kluis (scannen). Indien je de kluis voor meer dan 24 uur in gebruik genomen hebt, dan zal bij de afhaling van de inhoud het openstaand saldo betaald dienen
te worden alvorens je toegang krijgt tot de kluis.

[…]

WAT GEBEURT ER ALS DE VOORWERPEN NIET WORDEN AFGEHAALD ?

Voorwerpen die na 168 uur niet weggenomen zijn, worden ambtshalve naar de bagagebewaargeving overgebracht. Van dat ogenblik af gelden voor deze voorwerpen het tarief en de voorwaarden van “bewaargeving van bagage”.

Voorwerpen die niet binnen een termijn van 50 dagen worden afgehaald bij de “Bewaargeving voor bagage”, zullen beschouwd worden als “achtergelaten” en zullen overgemaakt worden aan de onderneming waarmee NMBS een recyclageovereenkomst heeft afgesloten (VZW Spullenhulp).

The rough translation by google says:

HOW DOES IT WORK ?

When using the safes you pay rent for a period of 24 hours. After the expiry of this period, or if the safe was opened by the customer during the rental period, it must be for a new period of 24 hours paid. The maximum period of use is 168 hours.

With the payment you will receive a ticket that you must keep for the reopening of the safe (scanning). If you have the safe have taken into use for more than 24 hours, the outstanding balance will have to be paid when the content is collected
before you get access to the safe.

[…]

WHAT HAPPENS IF THE OBJECTS ARE NOT COLLECTED?

Objects that are not removed after 168 hours are automatically transferred to the baggage claim. From From that moment on, the rate and the conditions for “storage of luggage” apply to these objects.

Items that are not collected within the 50-day period from the “Baggage deposit” will be considered “left behind” and will be transferred to the company with which SNCB a has concluded a recycling agreement (VZW Spullenhulp).

To be sure you can try calling the left luggage service at Brussels Midi and ask: 022248862

Airport Facilities

Brussels Airport (BRU)

The Brussels Airport website has a page on luggage storage services, mentioning dimensions, prices and maximum storage duration. To date there are two storage areas, one in the public area of the airport and one in the airside transit area.

PUBLIC AREA

Baggage lockers are available on level 0 on the left against the façade for anyone leaving the terminal via the exit bus station.

• The use of a locker cost € 7.50 per 24 hours.
• Payment is made with coins of € 0.50, € 1 and € 2.
• The change machine near the lockers accepts banknotes of € 5, € 10 and € 20.

Locker dimensions:
Width: 54 cm | Height: 89 cm | Depth: 80 cm

Oversized baggage

Oversized baggage can also be deposited on level 0. To do so please ring tel. +32 2 753 30 13 or use the interphone which is available free of charge near the lockers.

Storage costs € 7.50 for 24 hours for 3 pieces of luggage
For every extra piece of luggage € 2.50 will be charged.

TRANSIT AREA

Small luggage lockers are also available in the shopping area of Pier A, ground floor and 1st floor. These lockers can also be rented for short periods. The charge is:

• € 1 for 30 minutes
• € 2 for 1 hour
• € 3 for 2 hours
• € 5 for 24 hours

How Long Can You Store For?

The linked airport page says that the lockers in the public area of the airport can be used for an unlimited amount of time. However, after 72h the lockers are emptied and their content is moved to a dedicated storage area, from which they can be retrieved by getting in touch with the staff:

• Duration is unlimited. However, after 72 hours your belongings will be removed from the locker and stored in a storage room. To recover your belongings, please use the interphone next to the lockers and an attendant will hand them to you against payment of the balance due. The rate will be the number of days or part of a day multiplied by the daily rate of € 7.50

The same webpage says that lockers in the airside transit area of the airport can be rented for a short period of time, without any specification of the maximum duration of such rental.

Brussels South Charleroi Airport (CRL)

The Brussels Charleroi Airport website has a page on luggage storage which mentions automatic lockers which can be found outside the terminal next to the taxi rank. There is no mention as to the maximum rental duration.

Luggage storage

Automatic lockers are available outside the terminal, next to the taxi rank. You can leave any kind of luggage there.

The lockers are charged per 24hr period (the lockers accept EUR coins):

• Small locker = 5 €
• Medium locker = 7 €
• Large locker = 9 €