Dow Jones won the contracts after a bidding process and will pay $6.5m (£4.6m) to the company.
Bridge began selling the news contracts as part of its Chapter 11 bankruptcy, filed in February after it failed to secure new financing.
Angus Robertson, executive vice-president at Bridge, said, "It's time to acknowledge that BridgeNews as we have known it will be wound down in several weeks."
New York-based Bridge Information delivers data and news to customers' desktops via its internet service. It has 5,000 employees worldwide and more than 300,000 users in 65 countries.
Dow Jones has agreed to hire 10 members of the Bridge News staff as part of the deal. Dow Jones will also provide news to all current Bridge customers on an interim basis until other Bridge assets can be sold. The deal must be submitted to the US bankruptcy court for approval.
In March, Bridge sold a number of its businesses to US rival SunGuard Data Systems for $165m (£115m). Bridge received three bids for its assets from Reuters Group, Moneyline Network and Fin Info in April.