The investment is the biggest since the supermarket opened its doors in Shaw Ridge, taking over the space filled in the 1980s by French retailer Carrefour.
The store will remain open while work is ongoing and the revamp is expected to be complete in November.
An Asda spokesperson said: “We’re bringing lots of new offers to Asda Swindon West this year, with every part of the store receiving investment.
“Everyone is working hard behind the scenes to ensure there’s minimal disruption for our customers and the community.
“We’d like to thank them in advance for their patience whilst we make these exciting improvements to the store, which we hope to have completed in November 2020.”
A complete front-of-house transformation will see new concessions such as pan-Asian street food kiosk Panku launched, as well as the George clothing section moving to a separate unit outside the main store.
The store will also have an automated parcel collection and returns unit outside, as well as new ATMs close to the entrance.
Improved toilet facilities will be built on the ground floor, moving this from the current second floor location to allow for better disabled access.
Alongside these changes, Asda added that “every part of the store will be refurbished, including the tills, health and beauty and beer, wine and spirits sections.”
Swindon councillor for Shaw Mary Martin welcomed the store’s first significant investment since £2.8m was spent on an upgrade in 2010.
She said: “It’s really good to see a facelift of a local store, we use it all the time.
“One of the real big improvements is the toilets are now down in the mall which is a great advantage.
“At the end of it, it will be like new. It will be brilliant.
“When you use something every day you don’t notice if it is getting a little bit dusty round the edges, but I think what they’re doing will make a big difference.”
Coun Martin even believes the upgrade could attract more shops to the area.
She explained: “It’s really good for the area that the investment is being put in. It shows the commitment that this is a hub store for the community
“It would be nice to have more of a range of stores in the smaller units around and if there’s extra footfall and encourages people to open stores then that would be really good for the area, clearly.”
South Swindon MP Robert Buckland added: “I warmly welcome this significant investment into what is a vital shopping centre for local residents.”