"I think the family drive has helped this to happen, and we're excited," said Bernie Monk, spokesman for some of the families.
"It's positive news, but something we've been anticipating for quite a while but we just had to get the ticks in the right place.
"And there'll be a lot of work to be done before we can start walking up the drift."
Prime Minister John Key has pledged $10 million for the re-entry if the plan is signed off by Cabinet.
The re-entry plan also needs to be deemed safe by the Government's High Hazards Unit.
A spokeswoman for state-owned coalminer Solid Energy today would only confirm that the board has approved the sealing of the ventilation shaft, and that the plan had been passed on to the Minister's office.
Mr Bridges confirmed this morning that he is now considering the plan provided by Solid Energy, alongside advice he is getting from officials at the Ministry of Business, Innovation and Employment.
"Any decision on re-entry to the Pike River Mine drift is still subject to consideration by the Cabinet," he said.
"I am not prepared to put a timeline on this but we are moving as quickly as possible.
"As we have said before, in the end any plan to explore the drift must be safe - because more lives can't be put at risk - technically feasible and financially credible."
Families of the men have been fighting to get their bodies out since the disaster.
Progress had stalled until the families brought in their own international experts last November to explore potential methods of gaining entry to the drift.
Mr Monk, whose son Michael died in the tragedy, applauded the Government and Solid Energy for getting all interested parties round a table and "making things happen".
"We knew this could happen. Our experts we brought in from overseas told us this could happen and it finally has," he said.
"Once we get the tick of approval, and the money is made available to do the work, things will move pretty quickly."
As the only two miners to survive the disaster, Russell Smith and Daniel Rockhouse, were inside the drift when the explosions happened, he said there was a "possibility" that some bodies were lying in that area.
"There's 800m there unaccounted for. Russell and Daniel got out, so what's to say there weren't people further down. This plan is phase one, and that's all we're concentrating on at this stage."