The billionaire's umbrella company, Bristol Sport Limited, has also funded Bristol Rugby and Dino Zamparelli - a Clifton-based GP3 racing driver.
"We can help develop basketball and a first-class franchise here in Bristol," Lansdown told BBC Points West.
"It's given us a third string to our bow along with football and rugby. It will be a fantastic combination."
The BBL currently consists of 13 teams from England and Scotland, but will be expanding over the next two years.
BBL move excites Flyers captain Streete
The league is an independent company owned by its member clubs and there is no promotion and relegation to or from the second tier - the English Basketball League (EBL) and the Scottish Basketball League (SBL).
Bristol Flyers, established tin 2006, secured promotion to Division One in 2007 and were crowned champions four years later.
"It's very exciting for the city of Bristol and basketball as well," coach Andreas Kapoulas added.
"We're looking at a five-year plan to build a successful BBL franchise. Bristol Sport can enhance our model and produce a franchise that spectators will want to come and watch."
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