About 9.30am the group, in their late teens and early 20s, woke to find water entering the van where they had been sleeping under the bridge, Senior Constable Dave Colville said.
They tried to push the van out of the river, which had risen dramatically overnight.
''[But] unfortunately the two vans had been tied together to create a washing line and that prevented the group from pushing the first van out,'' he said.
As they started trying to empty the vans of their possessions, some items were washed away and one of the group swam after them.
"He was washed away in the current and ended up making it to the bank on the opposite side of the river.
"He then crossed back over the river and was located some way downstream,'' Mr Colville said.
The vans were last seen floating down the river.
One of the tourists, Steve Harper, told Radio New Zealand that he and three others, Annie Roth, Jim Marshall and Sarah Isaacs, had parked under the bridge to shelter from a storm.
The two couples, from America and Germany, were about 50 metres away from the water and had checked the river level before they went to bed on Monday night.
Mr Harper said they then woke in the morning to chest-high water.
"The van was starting to fill up, it was already to the seats. I immediately rolled down the passenger window and jumped out, tried to save whatever clothes I could and threw them on top of the van.
"Jim just ran by bashing on the window trying to wake us up saying `evacuate, evacuate, evacuate'.''
He swam after some belongings and was swept downstream before grabbing a branch and pulling himself to safety.
The rain put Nelson City Council on high alert, with the Maitai Valley Road at Sharlands Creek being closed for much of the day due to surface flooding.
But council spokesman Shane Davies said the worst of it should now be over and the road had reopened.
"We understand that the rain is easing, but often heavy rain in the river catchments can take a while to reach the lower parts of the river.
"We'll be keeping a close watch on things until the river levels have subsided.''
A Fire Service spokesman said there were about four callouts in Nelson about 6.30am, mainly for alarm activations due to weather, but since then they had been very quiet.
Mr Corbett said Wellington had also had about 30mm of rain this morning.
"We still have some rain to come through Wellington for the next few hours but even here [in Wellington] it's becoming a bit more patchy and should all start to clear away later today,'' he said.
A Fire Service spokeswoman said they had no major weather-related callouts for the Wellington region today.
Heavy rain in Christchurch caused surface flooding around the Avon River in New Brighton.
"It's just every time we get rain, it's what happens where there's low land levels following the earthquake. They get prone to surface flooding,'' A Christchurch City Council spokeswoman said.
Mr Corbett said that after today's heavy rain around central New Zealand, tomorrow should be a much finer day for most areas.
