The company bought 51% of Slovak Telekom in 2000 and has made an offer for the remaining stake, still owned by the government of Slovakia.
The government had planned to sell its stake in an initial public offering but pulled out after it received a bid from an unnamed strategic partner earlier in May 2015 - now revealed to be Deutsche Telekom.
"As the only operator in Slovakia with quad-play capabilities, Slovak Telekom is a highly attractive asset," said Claudia Nemat, board member for Europe and Technology at Deutsche Telekom.
"It is the market leader in fixed line, fixed broadband and pay-TV, as well as the second largest mobile player in Slovakia. Furthermore, it is the second of our subsidiaries to already offer an all-IP network, and with the recent introduction of its Magenta One converged fixed mobile services continues to be at the forefront of innovation within our group."
Under the terms of the agreement, €100 million of the purchase price will be set aside in an escrow account for a specific time.
According to Deutsche Telekom, the transaction will have no impact on group revenue and EBITDA. The acquisition of the remaining shares will however lead to an increase in earnings per share attributable to the shareholders of the company.
It added that the transaction eliminates the cash leakage from dividend payouts to minority shareholders.
The deal is not subject to regulatory approvals and is expected to be completed in the coming weeks.