The flats are owned by All Saints’ Anglican Church.
Three of the flats on the site were used by the Salvation Army for emergency housing and one was used for student accommodation by Selwyn College.
A ceremony was held by the church earlier this month to farewell the flats.
A new prebuilt 30m-long temporary accommodation building will be installed at the site.
Selwyn College chairwoman Anne Stevens said the temporary housing was necessary to accommodate students while renovations were done on the college. Renovations were expected to last no longer than two years.