The incident happened on the Yeadon Way service station at around 7.30pm.
The attacker, a male with his face covered by a scarf, appeared at first to be a customer.
But he forced the driver out of the taxi - an electric vehicle - after pulling a kitchen knife out and threatening him.
The male then got in the vehicle and drove off, resulting in a police pursuit of it down the M61 into the Greater Manchester area.
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The police helicopter was scrambled and followed the stolen vehicle, reporting its progress from above.
Police said the vehicle came to a halt in the Westhoughton area after it ran out of power at about 8.10pm.
A man was detained at the scene.