The 53-year-old former political adviser was admitted in March last year with coronavirus symptoms, before being placed in a coma.
He was driven by ambulance to the couple’s north London home on Wednesday.
The news was confirmed on Good Morning Britain on Friday morning.
Derek has been taken off all machines and breathing apparatus but will receive 24-hour care at the property, which Kate has adapted in his absence to make it more accessible.
Last month ITV broadcast Finding Derek, a documentary exploring Derek’s illness and its effect on their two children – daughter Darcey, 15, and 11-year-old son Billy.
It detailed their experiences during his illness and featured Good Morning Britain host Kate speaking to people suffering long Covid, NHS staff and other experts.
One scene saw her recall being told by Derek’s doctors that he was the most seriously ill person they had seen who remained alive.
In another, Kate was seen preparing for his possible return by making their home wheelchair-friendly.
She suggested they would have a “completely different dynamic” in their marriage when he is able to leave hospital.
Kate is also publishing a book, called The Power Of Hope, detailing “the raw and emotional story” of her husband’s illness.
During the first lockdown she posted weekly updates on Derek’s recovery to coincide with the weekly Clap For Carers.