The health department will receive £610m extra, while housing and local government – which funds social care – will get almost an extra £400m.
It is a contrast to the last budget which cut every department apart from health and transport.
Drakeford, the former first minister, added: “This is a good budget for Wales. But it will take time to reverse the damage inflicted on Wales over 14 long years of neglect from previous UK administrations.”
Most of the funding comes from the UK government, which gave the Welsh government a cash boost when Chancellor Rachel Reeves announced her budget in October.
But it is not clear how much money will be swallowed by the higher national insurance payments for employers that she introduced.
Welsh officials expect extra funding to cover the cost for public sector employers, but not for the private companies that provide many services, including businesses running care homes.
