The 18-kilometre submerged Fehmarn Belt Fixed Link is due to open in 2029 but has been beset by legal battles from conservationists and ferry companies.
German regulatory approval is “a historic milestone”, said the project's chief executive Claus Baunkjaer.
The tunnel will be one of Europe's largest infrastructure projects, crossing the Baltic Sea between the ports of Puttgarden in Germany and Rodby on the Danish island of Lolland, reducing road journey times to 10 minutes from an hour-long ferry ride.
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It is expected to cost 52.6 Danish kroner (€7.1 billion), with the four-lane, twin railway tunnel section built and paid for by Denmark alongside EU funding, linking Hamburg and Copenhagen in two and a half hours by train.
The idea of a permanent connection across the Fehmarn Belt was mooted almost 30 years ago, originally as a bridge, just as the eight-kilometre Oresund link between Copenhagen and Malmo in Sweden was readying construction.
While Denmark has already begun building work on the project, work on the German side was halted by legal obstacles.
Environmentalists raised concerns over the environmental impact, especially on reefs and porpoises.
Unlike other underwater tunnels, such as the Channel Tunnel under the English Channel, the Germany-Denmark tunnel will not lie under the seabed.
Instead the tunnel is to use hollow concrete sections that are to be submerged and placed in a trench dug into the Baltic Sea floor.
Ferry firms facing vastly reduced trade also took a dim view of the competition from road and high-speed rail.
However, the federal administrative court in Leipzig rejected their arguments.
The Luxembourg-based European Court of Justice is still mulling other complaints related to the project.