Danson, who became a millionaire when his business information company was sold to Informa last year, has paid an undisclosed sum for the stake and will provide "considerable experience and expertise", the magazine said in a statement.
He will work alongside existing chairman Robinson, the Labour MP for Coventry North-West, who bought the title in 1996 and was, until now, the sole shareholder in New Statesman Limited.
The statement from the New Statesman said: "Both Mike and Geoffrey are committed via this joint venture to continued investment in the magazine, to ensure its future as the country's leading political and cultural weekly.
"Geoffrey and Mike both wish to emphasise that they are committed to maintaining the editorial independence and integrity of the New Statesman."
The left-leaning news weekly, which is 95 years old this year, is currently without an editor following the abrupt departure of John Kampfner in February.
The title is understood to be interviewing for a replacement this week, with deputy editor Sue Matthias currently acting editor.
Candidates are thought to include Matthias; Neal Lawson, chairman of pressure group Compass and managing editor of journal Renewal; and Mark Seddon, the former editor of Tribune and currently diplomatic correspondent for Al Jazeera English.
New Statesman political editor Martin Bright is also thought to be a candidate.
Robinson is thought to have offered the job to Steve Richards, the Independent political columnist and former political editor of the New Statesman, but he turned it down.
News of the sale of a stake in the political weekly comes after the title posted a disappointing performance in the consumer magazine ABCs.
The latest audited circulation figures show sales of the New Statesman fell 12.7% year on year in the second half of 2007 to 26,208.
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