The stakebuilding by KKR in concert with with Friede Springer, the widow of the company's founder, and CEO Mathias Doepfner is aimed at taking the publisher private by the end of the year or in the first quarter of 2020.
KKR achieved a 42.5% stake with its tender to buy out minority shareholders and bought a further 1.04% on the market, putting it ahead of Friede Springer's 42.6% and Doepfner's 2.8%.
The buyout offer, at 63 euros per share, valued the business at 6.8 billion euros, representing a 40% premium to the share price preceding the June 12 offer.
Once private, Springer hopes to gain greater freedom to build its digital portfolio and look for acquisitions away from the eye of skeptical equity markets.
"The results from the offer provide a very strong foundation for the planned strategic partnership with KKR," Doepfner said in a statement.
"We will concentrate in the coming months on implementing and accelerating our growth strategy."
(Reporting by Anneli Palmen and Klaus Lauer; Writing by Emma Thomasson; Editing by David Goodman)