The price Bloomberg has agreed to pay is above the nominal $1 fee it was believed the magazine's owner McGraw-Hill was seeking when it kicked off an auction in July. BusinessWeek is projected to lose more than $40m from revenues of about $130m this year.
Bloomberg is likely to rename the magazine Bloomberg BusinessWeek, according to chief content officer Norman Pearlstine.
The move is an extension beyond Bloomberg's core business of supplying specialist computer terminals to the finance sector, which generates most of its revenues, but fits more closely with its news provision via TV, radio and online.
The company does already have a print magazine, Bloomberg Markets, but this is mailed to its 300,000 terminal subscribers and is not a newsstand or opt-in publication.
BusinessWeek's near one million-strong readership of mostly business and government professionals was attractive, according to Bloomberg president Dan Doctoroff.
Doctoroff said: "BusinessWeek helps better serve our customers by reaching into the corporate suite and corridors of power in government, where news that affects markets and business is made by CEOs, CFOs, deal lawyers, bankers and government officials who typically are not terminal customers."
Separately, that Bloomberg's rival Thomson Reuters is putting the finishing touches to a takeover of financial commentary service BreakingViews.com.
Financial Services
Bloomberg wins BusinessWeek magazine auction
NEW YORK - BusinessWeek, the 80-year-old loss-making weekly US magazine, is to be sold to financial news and data company Bloomberg for around $5m (£3.1m).