The two cities, which account for the majority of the country's economic activity, are nearly 70 kilometres (44 miles) apart but are currently served only by a 90-minute winding railway line on a route designed during the British mandate.
Road traffic can be badly congested at peak times, with the journey taking up to two hours.
The much-delayed new train service will shuttle passengers at up to 160 kilometres per hour from early 2018, minister Israel Katz told journalists during a tour of an underground tunnel.
Built under Israeli control in conjunction with Chinese, Italian and Russian companies, the new line is an important part of the "public transport revolution" under way in Israel, Katz said.
The service will also stop at Ben Gurion International Airport, 10 kilometres east of Tel Aviv.
At peak times, there will be four trains an hour in both directions.
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Israel Railways director Boaz Tzafrir said they expected 4,000 passengers during rush hour, 50,000 per day and more than 10 million a year on the new service.
Public transport in Israel is based mainly on buses, with no metro systems.
Its railway infrastructure is underdeveloped in relation to high population density, leading to significant congestion, a January report by the Organisation for Economic Co-operation and Development on the country's economy concluded.
Trains comprise just 6 percent of public transport, against 30 to 60 percent in many other OECD countries, the report said.
The fast line project was launched in 2004 by former premier Ariel Sharon, who died in 2014.
But work began only in 2010 because of pressure from environmental protection associations.
Project director Dror Sofero called the new line an engineering feat, with its 40 kilometres of tunnels and eight bridges.