That offer trumped a $270 million bid from Answers.com that was reported three weeks ago.
The Times and IAC/InterActiveCorp announced the deal late Sunday. IAC, which also operates the dating site Match.com, is controlled by media mogul Barry Diller.
IAC said Ask and About will continue to operate as separate sites and will complement each other. The Ask search engine can draw on content from About in answering those search queries, and Ask can boost traffic to About by directing more users there.
The Times purchased About in 2005 for some $410 million. About has suffered in the past year because a change in the way Google handles search results made About content harder to find.
In the April-June quarter, the Times took a $126 million after-tax charge against earnings to reflect the declining value of the About business.
In that quarter, revenue from About fell 9 percent from a year ago to $25.4 million. Its adjusted operating profit fell 30 percent to $10.2 million.
Although the Times had been upbeat over About's prospects, Times Chairman Arthur Sulzberger Jr. said the sale allows the company to focus on its core brands, which include such newspapers as The New York Times, the International Herald Tribune and The Boston Globe.
Times' stock fell 11 cents to close at $9.11 Monday. The shares are close to the 52-week high of $9.57 hit last week.
Shares of IAC, also based in New York, rose 42 cents to $51.92. They hit a 52-week high of $54.20 a month ago.