Windhorst, who rose to fame in the 1990s as a teenage computer prodigy, has the option to increase his stake to 49.9% in the team which finished in mid-table in 2018-19.
Tennor said it would increase investment in players for the team, enhance its digital strategy and market the team better globally.
Hertha, who play in the Olympic Stadium in Berlin, won the German league title twice in the early 1930s but have never had such success since the Bundesliga was formed in 1963. Their best Bundesliga season was when they finished as runners-up in 1974-75.
The investment comes seven months after the private equity firm KKR divested its 36% stake in the team.
In the 1990s, Germany's "teen tycoon" Windhorst was lauded as a symbol of a new pioneering spirit by Chancellor Helmut Kohl. But several of his companies folded when the tech bubble popped and his investments have seen a mixed performance.
H2O, one of French bank Natixis' asset management businesses, has come over scrutiny over its links to Windhorst and Tennor..
(Reporting by Arno Schuetze, Anneli Palmen and Alexander Huebner; Writing by Tom Sims; Editing by Riham Alkousaa/Keith Weir)
