The move combines the UK's second-biggest bus firm and the operator of Welsh and CrossCountry rail services with a business that carries five million train passengers a day in Germany.
Deutsche Bahn already has a presence in the UK running services including Chiltern Railways between London and Birmingham. The group is looking for increased scale through the deal to take advantage of liberalised European transport markets.
Deutsche Bahn was founded in 1994 as a successor to the German national railway. It is still 100 per cent state-owned but run for profit by its management and operates in more than 130 countries.
Sunderland-based Arriva operates bus services across the west of Scotland from a base at Inchinnan. Deutsche Bahn said the Arriva brand would be retained outside Germany.
The combined business would carry about ten million passengers a day and have revenues of more than 28bn a year.