The inquiry will be overseen by the Deputy Prime Minister John Prescott, with a final decision expected next year.
The plans for the tunnel, known as the New Tyne Crossing were submitted to Mr Prescott's office in May.
It includes the construction of a two-lane tunnel which would cross between East Howdon and Jarrow, near the existing tunnel.
'Common sense'
At an estimated cost of £139m, it will be built under the government's controversial Private Finance Initiative.
If it goes ahead, the new tunnel would be used only by southbound traffic on the A19, and the current tunnel would then be converted to take only northbound traffic.
Friends of the Earth (FoE) has been publicly opposed to the new tunnel and has welcomed the decision by the Deputy Prime Minister to hold an inquiry.
A FoE spokesman said: "It is a victory for common sense".
Letters sent
The Environment Agency has also had concerns about the effect of building work on the water quality of the Tyne.
The promoters of the tunnel, the Tyne and Wear Passenger Transport Authority, has said the tunnel must be built if congestion on the A19 is to be reduced.
No date has been set for the public inquiry, but the government said it will be "as soon as possible".
The Department of Transport has received nearly 800 letters about the controversial project.