The combined practice will trade under the Nightingale brand and will employ more than 200 architects and technical staff. Both firms form part of the Tribal Group.
The move follows Nightingale's takeover of Derek Hicks and Thew in November. The Liverpool-based practice will be officially relaunched under the Nightingale banner later this month.
Ash, which has offices in Dartford, Bristol and Leeds, has recently won a string of contracts, including a £22 million campus for Sutton Coldfield College and a £10 million complex for Solihull College.
The practice will also form part of the architectural and project-management framework for the government's flagship City Academies.
Development director Alistair Cory said acquiring Ash would enable Nightingale to assemble stronger bids for the government's £15 billion Building Schools for the Future initiative.
'It will allow us to go big on education, but not at the expense of healthcare,' said Cory.
He insisted rebranding Ash with Derek Hicks and Thew was essential to creating a straightforward identity.