The offer covers nearly all Toyota passenger cars and light commercial range, from the Aygo city vehicle to Land Cruiser and Hilux.
Two years ago, it was revealed that Volkswagen had cheated emissions tests that affected 11 million vehicles worldwide.
British drivers trading any brand of older diesel vehicle for a new Volkswagen will receive discounts of £1,800 ($2,300) on a compact model, £4,000 ($5,170) on a Golf, and £6,000 ($7,750) on a minivan.
For the electric cars in the firm's range, such as the eGolf, when combined with other grants on offer, potential buyers could get as much as €14,000 off the price.
For Audi the discounts range from £2,000 for the Audi Q2 to £8,000 for the Q7e-tron.
Toyota said it was offering up to £4,000 for buyers of a Land Cruiser, adding: "We go to great lengths to make sure [the old] auto is scrapped in the greenest possible way, with everything which can possibly be recycled being extracted by experts".
Several other major manufacturers have announced diesel scrappage schemes for the United Kingdom in recent months, including Toyota, BMW, Mercedes, Hyundai and Ford.
Most of the trade-ins can be of any brand of auto registered before 2010, the date when vehicles have had to comply with Euro V regulations on engine standards and cleanliness.
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The Kia scheme is open until the end of the year.
Scrappage vehicles must be registered by 31 December 2009 and be Euro 4 standard or older.
The government has floated the idea of a national scrappage scheme in its clean air strategy, while local authorities and the mayor of London have urged tougher action. It's the latest in a series of moves by German carmakers to fix the damage of the diesel emissions scandal.
VW's United Kingdom schemes follow those introduced in Germany which offer a discount of up to 10,000 euros (£9,000) to trade in diesel vehicles.
Lars Himmer, CEO of Volkswagen Group Ireland, said it was "particularly significant" that they are "actually going to take the qualifying vehicles off the road, with a Certificate of Destruction required to avail of the EcoGrant".
While cars traded in under the scheme will not necessarily be scrapped, customers will still be offered incentives of up to £5,000 off a new Nissan model, and savings of up to £2,000 to buy a used all-electric Leaf 24kWh.
Ana Nicholls, automotive analyst at the Economist Intelligence Unit, said the schemes were partly the results of pressure on carmakers to get polluting cars off the road.
To qualify, the vehicle has to be ordered by December 31 this year, registered by June 30 next and the trade-in needs to have been owned by the customer for at least six months.