As a result of the deal, Mitie will be less overly exposed to private sector contracts, which have worried investors as most companies continue to operate work-from-home policies for staff, meaning they do not need the company's services as much.
Both Interserve and Mitie ran Nightingale hospitals during the covid crisis.
Shares in Mitie gained 5p to 85p.
The deal leaves Interserve still with its RMD Kwikform division, a construction business and "Citizens Services" which runs probation services for the government.
The creditors aim to sell it all over the next 18 months, with analysts predicting RMDK is likely to fetch £250 million to £300 million.
Last year, Interserve's facilities management business made revenues of £1.4 billion and operating profits of £43 million.
Mitie also today reported operating profits of £86 million on turnover of £2.2 billion in the year to March. That was better than expected by City analysts.
Liberum analysts said "significant synergies" would be achievable from the takeover. They said the current trading had been more resilient than expected although working capital had been disappointing.
