The deal will be announced next week, the source said.
The touch-screen device, which combines the popular iPod music player, a video player and a Web browser, will be sold through Deutsche Telekom's retail outlets in Germany at an initial price of 399 euros ($554), the source said.
Deutsche Telekom's mobile communications unit T-Mobile has agreed to share voice and data revenues generated by the phones with Apple, the source said.
A T-Mobile spokeswoman declined to comment.
Speculation has swirled for months over which European telecom operators will sell the new phone, which has been available in the United States since the end of June.
Apple is expected to hand a UK sale deal to Spanish Telefonica's O2 UK unit, and a French deal to France Telecom's Orange, analysts say, though the companies have maintained strict silence about any deal.
Analysts are expecting initial exclusive transactions in the run-up to the key Christmas sales period to give Apple a share of data revenues and, in an unprecedented move, a share of voice revenues generated by the new phones.
Analysts had expected Vodafone to secure an exclusive, pan-European deal to sell the iPhone but media reports suggest it is now set to miss out.
This week Vodafone unveiled a range of new handsets and services for the key Christmas period including an exclusive music service offering unlimited tracks, to challenge the iPhone in Britain.
It did not disclose a price but a person familiar with the matter told Reuters it will be cheaper than T-Mobile's price for the iPhone.
Apple is calling a London news conference next Tuesday but has declined to give details. An Apple spokesman in Germany has said only that the company would announce which telecoms operators had won the sales deal by the end of September.
Apple signed up top U.S. telecoms operator AT&T Inc. (T) in an exclusive deal for at least two years to sell the phone in the United States.
It was not immediately clear if the European iPhone would be a 3G model. Analysts had expected Apple to launch a 3G phone in Europe after cutting the price of the U.S. iPhone, which is slower.
Earlier this month, Apple cut the U.S. price for the iPhone to $399 from $599. The company said on Monday it had sold its one-millionth iPhone, a few weeks ahead of schedule.