The controversial plan to close maternity services in north east towns caused an outcry.
Maternity units in Aboyne, Banff and Fraserburgh will close and be replaced by part-time units led by midwives.
Mr Kerr said it was important women should have a choice where to deliver babies when it was safe and sensible.
Mr Kerr said: "I am pleased that the board has concluded that there is scope for providing birth units for low-risk women in Aboyne, Banff and Fraserburgh. I now look forward to seeing the board take those plans forward.
"Of course, it will be for the board to determine the exact size and capacity of each unit, in accordance with local needs.
"I'm confident NHS Grampian will now go on to provide birth units which offer a safe and sustainable service for women in the Aboyne, Banff and Fraserburgh areas."
'Offer choice'
NHS Grampian chief executive Richard Carey said: "I am delighted that Mr Kerr has approved the final part of our proposals for health services in Aberdeenshire.
"Birth units in Aboyne, Banff and Fraserburgh allow us to offer the choice of a local delivery to women in these areas.
"I think it has been a very good compromise."
West Aberdeenshire and Kincardine MSP Mr Rumbles said: "This is a real victory for people power and I am delighted that both the minister and now NHS Grampian have accepted the arguments.
"I have nothing but praise for the campaigners."
'Great news'
Banff and Buchan MSP Stewart Stevenson added: "The mothers-to-be who previously elected to give birth in their communities rather than trek into Aberdeen will continue to be able to do so.
"That is great news for these mums and their children."
The Save Aboyne Maternity campaign (SAM) has called for each community to be involved in planning the arrangements.
NHS Grampian had recommended stopping the services over declining birth rates.
Campaigners fighting to save the services had made the "last throw of the dice" by meeting Mr Kerr.