The new facility will be located at Badgerys Creek, in western Sydney.
Planning and design work would start immediately, Prime Minister Tony Abbott said, with construction expected to begin in 2016. Funding would come mostly from the private sector.
The green light from Mr Abbott's government comes nearly 70 years after the idea was first debated.
The debate on the need for a second airport in Australia's largest city dates back to 1946. Badgerys Creek was a proposed site but the idea was then shelved for fear of backlash from local voters.
'Nationwide benefit'Around 20 sites were considered before the government approved the new facility about 45km west of Sydney's central business district.
Based on early estimates, the first flights in and out of the airport are not expected until the mid-2020s.
Speaking outside parliament in Canberra, the prime minister said Sydney's second airport would create up to 60,000 jobs when it became fully operational.
Mr Abbott has made it clear he wants a curfew-free airport. Sydney's current Kingsford Smith Airport is only 8km away from the city and it operates with a curfew between 23:00 and 06:00.
Australia's national carrier, Qantas, welcomed the announcement.
Chief Executive Alan Joyce said in a statement: "Sydney is the key gateway for air traffic in and out of Australia and the benefits of having two major airports will be felt nationwide."
"We look forward to being part of this process as Badgerys Creek moves closer to reality."