The broadcaster pushed the button, sending the hull sliding out from the Cammell Laird yard in Birkenhead, into the water where building will continue.
"Our future will be affected by what people working on this ship will be discovering in years to come," he said.
It is "the greatest possible honour" to be its namesake, Sir David added.
The hull of the £200m research vessel entered the river stern-first, creating a big wave as it hit the water.
Ahead of the launch, the riverbed was dredged in front of the slipway to make sure the steel mass did not bottom out.
When 100 years ago this country sent people down to the South Pole, we were the pioneers in exploring the Antarctic," Sir David said.
"When we did so, I suspect the reason we did was the South Pole seemed as far away as it could possibly get to be on this planet.
"Now, 100 years later, we realise that remote place is, in fact, key to the whole understanding of the planet. What goes on down there affects the whole of the Earth."
To read the full news coverage of the event please visit the BBC website