Under the investment, around €60m (£50m) of growth capital will be committed to building a regional data centre business in Germany.
It is the second deal under the firm’s Star III Fund, following the acquisition of Synergy Health Management in July.
As part of the deal, Peer Knauer, Star’s special adviser, will join the board as chair and invest alongside the company.
He said: “I am very excited to support the team in conjunction with Star to expand the business across Germany.”
Star managing partner Uniti Bhalla said: “This transaction continues Star’s successful track record of identifying capital-intensive businesses that have the potential to generate long-term and highly stable cash flows.
“We look forward to working with the team to significantly grow the infrastructure owned and operated by Globalways and are pleased to be able to continue our long history of investing in the German market with this differentiated strategy.”