Robinson, who is close to Gordon Brown, bought the title out of administration in 1996 and sold a 50% stake to Danson in April 2008.
The deal also gave Danson the right to buy the remaining 50%, which he has now exercised.
Danson said: "My arrangement with Geoffrey has been working very well, and we both agreed that the time was right for me to take full control of the New Statesman as we seek to continue to develop the title."
The value of the deals has not been disclosed, though Danson is unlikely to have paid a premium as the title was said by Robinson yesterday to be "going through a rough time" and breaking even.
Robinson will stay involved with the title as co-chairman alongside Danson, who made his fortune by floating and then selling Datamonitor to Informa.
Robinson said: "It was always my intention to pass full control of the business to Mike. I am very secure with the magazine being in his hands, both financially and editorially."
The New Statesman was first published in 1913 with an initial subscription list of 2,300 readers.
The circulation of the magazine is now 23,128 copies according to ABC figures for the second half of 2008.
Its right-wing rival The Spectator, owned by millionaires Sir David and Sir Frederick Barclay, has a circulation of 77,146.
Danson was closely involved in the appointment of the magazine's new editor, former Observer journalist Jason Cowley. Cowley joined last autumn from literary magazine Granta.
Cowley replaced John Kampfner, who oversaw a wide reaching redesign of the title.
Since the new editor's arrival a number of staff have quit. Most recently the New Statesman's political editor Martin Bright exited.
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