"It has been designed with children and their whānau at the centre while allowing for the provision of high-quality services, as well as encouraging clinical collaboration and communication."
The new hospital will have 50 beds and 21 clinic rooms spread across three floors.
In July last year, then Health Minister Jonathan Coleman said a gesture of the scale Dunajtschik had made was "extremely rare".
"Mr Dunajtschik has said his philosophy is that people blessed with a sound mind and body can look after themselves but those born with or suffering illness and disability need our support."
Clark said the Capital and Coast DHB's plans for a new children's hospital were brought forward last year following the announcement of Dunajtschik's donation.
"International evidence shows that health systems with a strong publicly funded core deliver the best health outcomes for all.
"I acknowledge that those outcomes are improved further with the incredibly generous support of New Zealanders like Mark Dunajtschik."
The Government's $45.6m spend on the new hospital comes from the $750m in Budget 2018 earmarked for the health sector.
Other funding announcements from that Budget line include $275m for Auckland DHB to address "significant infrastructure challenges" at Auckland City Hospital and Greenlane Clinical Centre.
Some $200m was set aside for a new elective surgery unit at Waitematā's North Shore Hospital.
Northland's Whangarei Hospital received $24m for a new endoscopy and cardiac care capacity and $8m was made available for Individualised Service Units at Capital and Coast DHB for people with disabilities.
The minister still has $200m left to allocate.
