But residents of border towns will be able to apply for exemptions to travel for work and essential health services.
NSW Police Commissioner Mick Fuller said the closure would be enforced on the NSW side from Tuesday 11:59pm.
He said there would be delays getting over the border for the first three days.
"The reality is, in the first 72 hours from midnight Tuesday this week, it will be difficult - not impossible - but difficult to make that crossing," he said.
"There will be delays whilst we work through who are essential workers."
He said Service NSW would open an online application by Tuesday for people to apply for an exemption.
Mr Fuller said the operation would be carried out by NSW Police with assistance from the Department of Defence, and later on, from other emergency services.
He said they would be focusing on the four primary arterial roads, but would also use drones and other aerial surveillance to monitor the border.
NSW Premier Gladys Berejiklian said anyone who felt they would be impacted by the closure could apply for a permit through Service NSW, including for work or access to healthcare.
But she asked border communities for "patience" as it would take two to three days to get the system in place.
Ms Berejiklian said she wouldn't put a timeframe on the border closure.
Victorian Premier Daniel Andrews said said it was a joint decision made by him, the NSW Premier and Prime Minister Scott Morrison on Monday morning.
“All of us agreed the best thing to do would be to close the border,” Mr Andrews said.
Mr Andrews said it would be enforced on the NSW side, which would free up Victorian resources.
“This is one of those things that I think will help us – in broader terms – contain the spread of the virus,” he said.
He apologised for any inconvenience the rule would cause people who have to travel to NSW.
In the last 24 hours, 127 cases of COVID-19 have been diagnosed in Victoria, and a man in his 90s died from the virus.
There are now 31 people in hospital, with five in intensive care.
More to come.