The company informed customers via email that it will stop taking orders on 22 May, after 12 years of trading.
The £200m takeover, which was reported by BigHospitality in December 2016, was investigated by the UK competition watchdog.
The investigation followed concerns from the Competition and Markets Authority (CMA) that the deal could result in worse terms for restaurants using either company due to the similarity of their services.
Just Eat was given the green light for the acquisition late last November, and the deal was confirmed in February.
Since then, HungryHouse says it has been “working with Just Eat to unite our restaurant partners and technology in order to provide the best possible takeaway experience in one place”.
The company says that a “vast majority” of its partners and customers already use both companies, and most restaurants will be available through Just Eat by 22 May.