The amount was pledged over three years, and was aimed at helping 10.7 million people in need. The UN has previously said it hoped to raise $1.5 billion in 2017 for the region, which includes Nigeria, Niger, Cameroon and Chad.
The United States, whose new administration has said it intends to slash its development aid budget, was not among the 14 countries that pledged money in Oslo.
"The US said they would come back with their contribution, so it is not factored in" to Friday's sum, Norwegian Foreign Minister Borge Brende said during a press conference.
Of the $672 million announced on Friday, $457 million has been earmarked for 2017 alone.
UN Under-Secretary General Stephen O'Brien said he was optimistic the overall target of $1.5 billion for the year would be met.
"In one morning we have raised a third of that," he said.
The eight-year conflict between the Nigerian army and Boko Haram militants has devastated the region.
With the sums pledged, "we're only touching the tip of the needs. Nevertheless we're hugely grateful," Nigerian Foreign Minister Geoffrey Onyeama said.