The deal, first reported by Sky News, was confirmed on Monday.
TBG, which is based in Zurich, will fund the acquisition through DTN, a company it acquired last year from the industrial powerhouse Schneider Electric.
It follows a troubled period for MeteoGroup under the ownership of General Atlantic (GA), which initially invested in it in 2013.
The deal is expected to enable TBG to expand its presence in the growing market for weather information services and technologies.
MeteoGroup chief executive Donat Retif said: “We welcome the new owner who has significant experience in metereological intelligence.
“The proposed acquisition will enable Meteogroup to deliver on its strategy and capitalise on a vast global market opportunity.”
MeteoGroup, which employs more than 100 meteorologists, has been a rare poor investment for GA, which has been a serial backer of technology “unicorns” such as Buzzfeed and Uber.
The value of the deal was not disclosed, but insiders said that it would crystallise a loss for GA. It is expected to complete next month, subject to regulatory approval.
Pricing pressure across the industry is said to have been a factor in the challenging conditions faced by the business in recent years.
MeteoGroup is a major supplier of weather forecasting information to business customers, competing with companies including StormGeo and IBM, the US technology giant which owns The Weather Channel.
Clients include British Airways, which uses its data on its in-flight entertainment system, and the BBC, where it replaced the Met Office as the principal supplier of weather-related data earlier this year.
Accurate weather data has become an increasingly important element of business planning processes for companies around the world.