The house, which is being furnished, is located in posh Green Avenue in the city, a statement issued by the MP's office said.
Mr Singh had defeated senior BJP leader Arun Jaitley in the just-concluded Parliamentary polls.
The statement said Mr Singh will soon set up his regular office at 4 Court Road in the city which will be manned by his permanent staff.
Yesterday, Mr Singh had tendered his resignation as Patiala MLA to Assembly Speaker Charanjit Singh Atwal after he was elected as an MP.
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