Up to 500 men aged 18-65 will be housed on the barge while they await the outcome of their asylum application.
The floating accommodation block was docked off the Dorset coast nearly three weeks ago, and has been empty since due to health and safety worries.
The government has said the vessel offers basic and functional accommodation and it previously housed oil and gas workers - as well as asylum seekers in other countries.
However, the key difference is that its capacity - which used to be 222 - has been doubled to 500 by putting bunk beds in its cabins, and converting some communal rooms into dormitories for four to six men.
Asylum seekers would be on the Bibby Stockholm "imminently this week, in the coming days", Ms Dines told the BBC's Radio 4 Today programme.
She said the increase in the number of people on the ship would be "gradual", with a possible 500 by the end of the week, despite concerns from the Fire Brigades Union that the vessel had originally been designed to house around 200 people.