Part of Ysgol Glan Clwyd in Saint Asaph will be demolished in November, with new classrooms, assembly, music, drama and dining areas created.
Work is aimed at meeting growing demand for Welsh-medium education.
Denbighshire council's cabinet will be asked to approve awarding a contract for the work to Willmott Dixon.

Its new official forecast is for the gap between spending and taxes still to be a deficit of £7bn in 2019-20, compared with the Office for Budget Responsibility's forecast made at the last budget for a surplus of £7bn.
Its gloomier projection may be seen as a particular embarrassment for the Tories, given that unlike Labour and the Liberal Democrats they are committed to generating a surplus on the overall budget.
However a small part of the forecasting difference between the IMF and the OBR is that the IMF assumes there will be a weakish minority government after the election and therefore spending will be a bit higher than the Tories' plan.
So a senior Tory put a brave face on the IMF's disagreement with the OBR and said it showed the risks of voters not giving them a clear mandate.
However that is not the whole story, in that the IMF also believes the OBR is being a bit too optimistic about growth and tax revenues in the latter years of the next parliament.
In truth therefore the IMF is highlighting that whoever leads the next government may be forced to increase taxes or cut spending a bit more than currently planned.
This may represent a bigger headache for the Tories than Labour or the LibDems given that in the last few days the Tories have committed themselves to £6bn of tax cuts and £8bn of increased spending on the NHS, without saying where the money for these giveaways would come from.
In fact just yesterday a senior Tory pointed to the OBR's projected surplus for 2019/20 and said that would cover (almost) the NHS commitment.
Well the IMF today says that £7bn surplus is a chimera.
All that said, the IMF forecast is a million miles from being devastating for any party: the difference between a £7bn deficit and £7bn surplus in 2020 is just 0.6% of GDP or national income - which is a rounding error in the context of a deficit that was a humongous 10% of GDP just five years ago.

The man, in his 30s, was found with chest injuries in the red Mazda in North Way, Barton, just after 22:45 BST on Tuesday. He later died in hospital.
Police said 34-year-old Rafal Stawski of Mayfair Road, Oxford, had been charged with one count of murder.
A 31-year-old man, from Oxford, also arrested in connection with the man's death has been released without charge.
Mr Stawski is due to appear before Oxford Magistrates' Court.

Anton Levin, from Dagenham, was stabbed at a house in Southend in November 2014.
Abdulfatah Suleiman, 28, was arrested in Norway and extradited back to the UK where he was convicted by a jury last month.
He was jailed for 16 years with a five-year extended licence.
Live updates on this story and others across Essex
Chelmsford Crown Court heard the 24-year-old's death involved rival drug gangs. Three others were convicted last June for their role in his killing.
Danielle Russell, 27, from Southend, and two teenage boys were found guilty of manslaughter, conspiracy to commit GBH and conspiracy to commit robbery.
Russell was jailed for 11 years, and the teenagers, who cannot be named, were given detention orders for ten years and four months with a five-year extended licence.
Suleiman, who was also found guilty of robbery and unlawful wounding, was arrested in Norway at the conclusion of their trial.
Following the sentencing, Anton's mother said she was "very disappointed" that Suleiman had not been convicted of murder.
"He had the knife and he killed my son Anton Levin.  He has been jailed for 16 years but I would have preferred that he had been jailed for life.
"I hope he thinks about the harm and distress he has caused me and my family. But this will never bring my son back," she said.
A £15.9m Denbighshire school construction project is set to get under way after a firm was chosen to carry out the work.
[NEXT_CONCEPT]
The International Monetary Fund has today highlighted the challenge to be faced by the next government in returning the public finances to balance.
[NEXT_CONCEPT]
A man has been charged with the murder of a man found fatally injured in parked car in Oxford.
[NEXT_CONCEPT]
A man who fled the country after stabbing a university graduate to death in a row between rival drugs gangs, has been jailed for his manslaughter.