Transport for London (TfL) said the deal - which could be extended by a further two years - will see the firm operating all London Overground routes from 13 November.
Arriva will take sole charge of the rail network as Arriva Rail London, after it held the previous contract in a joint venture with MTR under the company London Overground Rail Operations Ltd.
TfL said the firm will be expected to deliver significant improvements to the London Overground, which carries about 585,000 passengers a day and has seen numbers rise 400% since 2007.
The announcement comes after Arriva - which operates bus and rail services across 14 European countries - was awarded the Northern franchise by the Department for Transport, which starts on 1 April.
Gareth Powell, TfL's chief operating officer, said: "We have worked hard to deliver major improvements for our customers, taking a neglected part of the transport network and transforming it to support new homes, jobs and economic growth across the capital.
"Arriva will build on this by extending operating hours, improving frequencies and introducing new trains."
Arriva - the UK transport division of Deutsche Bahn - secured the contract after fending off rival bids from Metroline Rail Limited, MTR Corporation and LoKeGo, a joint venture between Keolis (UK) and Go-Ahead Group.
TfL said the company will help deliver new trains on the Gospel Oak to Barking line and on to routes out of Liverpool Street.
Passengers will also see extended operating hours, while new services will be introduced on some routes over Boxing Day, TfL said.
However, the award of the contract would be subject to a 10-day standstill period.
Chris Burchell, managing director of Arriva's UK trains division, said: "It is exciting to be given the opportunity to build on the major improvements we have made in recent years and we are delighted to be playing a key role in the next phase of London's growth and development."