The appointment of Cowley, a former literary editor of , comes three months after his predecessor John Kampfner resigned.
Kampner's departure followed a row with owner Geoffrey Robinson MP, believed to be over the issue of investment in the title.
Robinson subsequently sold a founder Mike Danson.
Cowley, who joins in the summer, said he was tempted away from Granta by Robinson and Danson's vision for News Statesman.
He said: "Under my editorship the New Statesman will further strengthen its unique inside coverage of the UK's political scene and demonstrate a more vital, urgent and internationalist tone and sensibility."
The left-leaning magazine recently suffered a 9.8% drop in its circulation over six months. Its July-December 2007 circulation was down to 26,208, around 500 copies behind more high brow rival Prospect. Rightwing political rival The Spectator has an ABC figure of 75,633.
Robinson said: "[Mike and I] both agree that Jason has all of the talents we wanted and we are looking forward to welcoming him to the team."
Danson said: "His energy and expertise lend themselves to our plans for growth here in the UK and internationally.
"The New Statesman is a magazine that is always in the spotlight and Jason has the experience and qualities to take it forward."
Sue Matthias, the deputy editor, had been acting editor since Kampfner left and was one of those in the running for the job.
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