The bones have been gifted to North Sunderland Parish Council by Northumberland County Council.
It plans to put them at the harbour where they would be seen by lots of visitors, along with an information board detailing the port’s fishing heritage.
However, Seahouses Primary School claims the whalebones were originally gifted to the school and should be kept on its grounds.
Headteacher Vicky Allen says she is ‘extremely disappointed’ at the outcome.
In a statement read out at a parish council meeting, she said: “Myself and the governors of Seahouses Primary School were extremely disappointed with the consultation outcome.
"I find it really frustrating as to how the parish council can be given custody of them when we have the evidence that they were a gift to the school.
“I want everyone to know that we did not stop fighting for the whalebones. I think it is such a shame that they have been taken away from their intended recipient, the local schoolchildren.”
The whalebones were in the grounds of the former first school until they went missing in December 2018, later found dumped near North Sunderland Football Club.
Rachel Shiel, vice chairman of governors, said: “When we were on the previous site, one of the stipulations we made was that the whalebones would be shifted to the new site with us.
"As we all know they weren’t moved and they were stolen and dumped. From that point we were contacted to ask if we wanted them and the governing body was unanimous that we wanted to keep them with the school.
"We have never changed our view on this only to discover that the whalebones are no longer in the school’s possession. They don’t belong to anyone else and we have the ledgers as proof.”
For the past year they have been in storage but Cllr David Shiel got permission to collect them last week and they are now at the harbour pending a decision on what to do next.
Cllr Sylvia Hillan said: “We asked if we could have them for the harbour and after many months we were told we could.
"We were told the school wanted a plaque put on to say they had been kept there for some years and that when we have a ceremony the children could be invited.
"As far as we knew, the school knew all about it. The county council has gifted them to us and that is as much as we know.”
Cllr Guy Renner-Thompson, local county councillor, added: “As far as the county council is concerned the issue is closed. They know the school and parish council wanted them and they have come down on the side of the parish council.”
The bones are believed to be those of a Greenland right whale and are likely to have been brought back by one of the Berwick whalers in the 1820 or 1830s.
They lay in a farm barn in North Sunderland for many years before being erected at the school in the early 1930s.