The $3.93 billion cash-only sale, which values Postbank shares at 25 per cent above their closing price yesterday, would effectively double the bigger bank's customer base in Germany.
Under the terms of the deal, Deutsche Bank is to retain the choice of whether or not to buy up an additional 18 per cent before 2011.
The 30 per cent stake was previously held by Deutsche Post.
Moves to consolidate the German financial services industry are likely to meet with government approval.
Speaking at a banking conference yesterday, finance minister Peer Steinbrueck said: "There's no alternative to consolidation in the German banking sectorâ¦we need to do this to stay competitive and to be able to gain access to the benefits of international capital markets."
Deutsche Bank is Germany's largest bank.