The new Metrolink 5.5km (3.4 mile) line will go from Pomona to Trafford Park via the Imperial War Museum.
Transport for Greater Manchester (TfGM) submitted the plans to Transport Secretary Chris Grayling following a public inquiry last year.
Now it has been approved, construction work could start by the end of the year and the line may open in 2020.
The Trafford Park line will call at six new tram stops - Wharfside, Imperial War Museum, Village, Parkway, EventCity and the Trafford Centre.
Greater Manchester interim mayor Tony Lloyd said the new line would "boost our economy and bring us closer to our goal of a world-class transport system."
He said it could create thousands of new job opportunities "as well as offering fast, frequent and sustainable links to some of the city-region's greatest sporting and cultural venues as well as the Trafford shopping centre".
Trafford Council leader Sean Anstee said: "Excellent transport links are vital to make Greater Manchester as attractive as possible for businesses to establish themselves here and, with them, more jobs and apprenticeship opportunities."
TfGM said 89% of people were in favour of the extension plans in a 12-week public consultation in summer 2014.
Funding has already been secured by Greater Manchester Combined Authority through the "earn back" funding arrangement as part of the Greater Manchester devolution deal, said TfGM.
The extension will increase the size of the Metrolink network to more than 106.5km (66 miles).
A £350m tramline to Greater Manchester's Trafford Centre has been given the go-ahead by the government.