The group now jointly owns a 25.9% stake in the agency worth £22m.
Purplebricks used the purchase to notify investors that the company is trading in line with expectation for the current full year.
Homeday launched in 2015 with a digital estate agency model.
The management team will continue to run the business under the Homeday brand, with added support and expertise from Axel Springer and Purplebricks.
Purplebricks said the Homeday model has some similarities to its own, by combining a technology platform with an expanding number of local agents.
Europe’s second largest market
Michael Bruce group chief executive of Purplebricks said: “Our investment in Homeday secures for us a strong foothold in Europe’s second largest residential real estate market.
“This is a good opportunity for Purplebricks, allowing us to partner early with a dynamic and committed management team, while remaining focused on realising the opportunity in our existing markets.
“Steffen Wicker and his colleagues at Homeday share many of our own values and have a clear ambition to become Germany’s leading online real estate agent by providing a trusted and transparent service to customers.”
Germany represents one of the largest residential real estate markets in Europe, with more than 600,000 annual sales transactions, according to Purplebricks.
Bruce added: “I am pleased to report that we continue to perform in line with our expectations and make further gains in market share despite what are challenging market conditions in the UK real estate sector.”
In July Purplebricks announced it was expanding into Canada with the takeover of online agent DuProprio/ComFree (DPCF).