Teignbridge District Council said the 30ft (9.1m) fin whale, which was found on Red Rock Beach near Dawlish, will be removed by contractors.
The London Zoological Society has taken samples from the whale as part of a research project into strandings around the UK.
People again turned out to see the whale, which has been cordoned off.
More on the washed up whale, and other Devon and Cornwall news
The council, which has begun work to remove the whale, has advised members of the public not to approach the badly-decomposed carcass.
Councillor Humphrey Clemens said: "This is a very unusual and unfortunate situation and it's not going to be an easy job.
"We would ask people to respect the cordon around the whale and keep their dogs on a lead."
A council spokesman said it would know the cost "when the removal has been complete".
She said: "Our focus right now is doing the job carefully, safely and appropriately. We will, of course, look to recover costs where we can."
A dead whale which washed up on the Devon coastline will be removed at the weekend.