Mr Obama ordered federal aid for three of the worst affected counties following a request by Governor Earl Ray Tomblin.
Residents will now receive grants for temporary housing and repairs.
More than 30,000 homes and businesses are without power.
Heavy rain on Thursday turned rivers and streams into torrents, cutting off several towns.
The floods are the worst in a century in some areas and hundreds of people have had to be rescued.
President Obama "ordered federal aid to supplement state and local recovery efforts in the area affected by severe storms, flooding, landslides and mudslides", a White House statement said.
Mr Tomblin said the federal help included medical support and housing to Kanawha, Greenbrier and Nicholas counties.
Officials were still assessing the damage in other areas and additional requests for aid could follow, he added.
West Virginia deadly floods: Obama declares major disaster
26 June 2016
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US President Barack Obama has declared a major disaster in the state of West Virginia, where the worst floods in more than a century have left at least 24 people dead.
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