The financial terms of the deal have not been disclosed. Kroenke's purchase of a controlling interest is expected to close early next year, pending Major League Baseball's approval, said a club statement.
"The Angels are a storied franchise anchored in a great market. We look forward to an exciting future with the Angels organization," said Kroenke, in the statement.
The Angels play in Anaheim, a city near Los Angeles, and were previously owned by the Walt Disney Company.
Current owner Arte Moreno said the "Angels organization is pleased to announce this transaction with Kroenke Sports & Entertainment".
"The Moreno Family has been honored to steward the Angels for 23 years and we believe with KSE's experience and success they are the best next owner for the franchise," he added.
The Angels won their sole World Series title in 2002.
Despite the presence of superstars Mike Trout and - until he moved to the Los Angeles Dodgers in 2023 - Shohei Ohtani, the Angeles have not even reached the playoffs since 2014.
Long overshadowed by the neighboring World Series champion Dodgers, the Angels are on course for their 11th straight losing season.
Kroenke made his fortune in real estate, and is married to an heiress of the Walmart retail empire.
Through his holding company US billionaire Kroenke also owns the Denver Nuggets NBA basketball team, the Colorado Avalanche NHL ice hockey franchise and the Colorado Rapids MLS soccer outfit.
