The house will be sandwiched between an office block and a pub in Euston Road, in a former alleyway which once provided access to the now-demolished Royal Orthopaedic Hospital.
Developer Bolsover Street says the plans will help provide "family-sized housing in the city" and the proposals have been approved by Westminster Council.
When built, the narrow home will feature a ground-floor courtyard at the back, as well as a roof terrace facing Euston Road.
There will also be an open plan kitchen/diner on the ground floor, a first-floor living room, three bedrooms and two bathrooms.
In a planning statement submitted to the council, the developer states: "This narrow site can be opened up to deliver a family-sized home with private outdoor space, supplemented by the range of recreational opportunities at Regent's Park."
The application was opposed by the freeholder of the Green Man pub, next door to the site.
In a letter of objection to the council, they stated: "The insertion of a high value residential unit ... sandwiched between two commercial properties would be inappropriate, not only because it is entirely out of character and context of the area, but also because it is a contrived residential unit forced into a space designed as a narrow service road."