The supplies, worth at least $500,000, were uncovered in two Rosebery storage units on Wednesday afternoon about 24 hours after going missing from a Botany freight depot.
Images released by police on Thursday show dozens of boxes of the Chinese-made tests and KN95 face masks inside one of the units.
The 27-year-old man was arrested at Mascot police station on Wednesday night and charged with dishonestly obtaining property by deception.
He's been refused bail ahead of an appearance at Central Local Court on Thursday.
Three men arrested at the storage unit on Wednesday were released from custody after being interviewed.
Police say inquiries are continuing.
The theft comes amid a nationwide shortage of the kits and some retailers charging exorbitant prices.
Australian Competition and Consumer Commission boss Rod Sims says the agency has received reports of RATs costing up to $500 for two tests through online marketplaces, and more than $70 per test through convenience stores, service stations and independent supermarkets.
Despite wholesale RAT costs being up to $11.45 a test, the agency said prices for the kits are often retailing between $20-$30 and are priced much higher through smaller outlets.
The Therapeutic Goods Administration is also investigating some businesses found breaking up packs of multiple RATs so each test can be sold individually at a higher price.
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