The former school site is bounded by Polton Street, Moorfoot View and Moorfoot Place.
Subject to final planning approval, Midlothian Council plans to build a new intermediate care facility and new extra-care housing on the site.
The existing infant school building will be retained, and will be refurbished to provide day care, meeting and office premises.
Council leader Derek Milligan (Lab) said: “A full planning application for the proposed care facilities and new housing development was submitted earlier this week. The demolition work is a key first step being taken to prepare the site for the planned redevelopment."
“The proposed intermediate care building will provide short term accommodation as well assessment, rehabilitation, interim and respite care provision,” added Councillor Milligan.
“The extra care housing development will offer 44 tenancies and support for older people and those with a variety of degenerative conditions.”
As part of the pre-application consultation, two online public events were held in April to give local people the opportunity to hear about the proposals and to ask the design team questions.