Mathiesons, which was established in 1872, will sell three of its Bavarian fresh cream and fruit flavoured tarts at 289 stores in England and Wales.
The tarts are currently stocked in 56 stores in Scotland.
The contract means that 2.9 million Bavarian tarts will be produced at its Larbert production facility in the Central Belt every year, up from 107,000 currently.
Mathiesons' sales director Lorna Love said: "This is a very exciting opportunity which will bring our products to a much wider audience"
In May 2012, majority shareholder Pemberton Capital agreed a deal with administrators from KPMG to buy eight stores and the main bakery to focus on selling to wholesale customers such as the main supermarket chains.
However, 20 shops were closed and 84 people made redundant.
The bakery currently employs 200 people.
Lisa Prudhoe, Asda's customer planner for Scotland and Northern Ireland, said: "As part of our strategy, we place huge importance on supporting local suppliers.
"Mathiesons is the perfect example of how Asda are able to support and nurture the businesses of local Scottish producers, their range of cakes and confectioneries are the perfect sweet treat and we're confident our customers in England are going to love them."