The work, which will involve drilling and grouting old mineworkings and strengthening slopes and the river banks, will take four years, the council said.
The company has said it is mainly interested in mining in areas of rock between existing flooded mineworkings, but some of those flooded areas need to be pumped for safety.
The Mines Rescue Team leader Andrew Watson said no contact has yet been made with the miners, who were trapped by water after they broke into an area of old mineworkings.