"set up residence" is a grammatically correct and usable phrase in written English.
You can use it to refer to the act of someone taking up permanent residence in a particular place. For example, "John and his family moved to London and set up residence there."
(Gupta recently set up residence in Florida, which would protect his home).
Arriving in Manhattan, the fêted inventor set up residence in the penthouse of the Plaza Hotel.
Before he died, East Lynne set up residence at the Frankin Street School.
Sometimes it is the broker who discovers that, say, a vagrant has set up residence in a vacant property.
His rivals say he set up residence here in 1996, when he was elected national president of his party.
Like thousands of others displaced by fighting in the province, Mr. Saeed and his family set up residence in decrepit public school buildings.
As a Canadian, I was impressed by your construction of affordable housing during the big snowstorm, and like you, I was taken aback when the housing office said that setting up residence in igloos was forbidden.
Following scandals more than a decade ago over the "Sark Lark", the group scattered, setting up residence in far-flung jurisdictions such as Cyprus, Dubai, Vanuatu, Mauritius, or Nevis in the Caribbean.
He then sets up residence in a city that, though clearly fantastical (a white Pac-Man-like creature infests his apartment instead of cockroaches), resembles New York's historically ethnic neighborhoods.
The archdiocese had already set up a separate seminary residence in Riverdale, the Bronx.
Lucky, then, that the two institutions merged in 2011 and set up permanent residence in this light-flooded, loft-like gallery with rooftop deck.
