The 15-year-old attacking midfielder will join a side whose attacking limitations were harshly exposed by Italy, who beat the Norwegians 2-0 in Oslo in their opening qualifier in September.
Despite having more possession than the Italians, the home side did not manage a single shot on target, disappointing the sold-out crowd hoping for a good start to the campaign.
"Martin has performed at a high level for a longer period," Hogmo told a news conference in Oslo.
"He has shown quality in the Tippeligaen and he created chances on his debut."
Odegaard became Norway's youngest player when he made his debut in a friendly against the United Arab Emirates in August at the age of 15 years and 253 days.
The playmaker's exciting dribbles and incisive passes for Stromsgodset have attracted the attention of top clubs like Barcelona and Bayern Munich, and scouts have been flocking to Drammen, just outside Oslo, to watch him.
Second-bottom of Group H, Norway are away to bottom side Malta on Oct. 10 before hosting Bulgaria.
(Reporting by Philip O'Connor, editing by Ed Osmond)
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