Yes. But "on which the new house has been built" is better. I would change "foundations" to "foundation".
Student or Learner
Can I say as follows:
The ancient foundations which the new house has been built on was made of stone.
...or 'The ancient foundations...were made of stone'.
And in BrE, it sits on its foundations.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.