The retailer's director of brand communications Claire Harrison-Church said the change reflects the pressures being put on its customers.
She said: "We know that customers' budgets are under more pressure than ever before but when we speak to our customers they talk about not wanting to compromise on the quality of products."
The shift in brand proposition is the result of an 18-month review and overlaps with the end of the partnership between the supermarket and long-term brand ambassador Jamie Oliver.
It will be illustrated with a new ad campaign breaking tonight that shows how customers can gain from enjoying the small things in life. It was created by AMV BBDO with media planned and bought by PHD.
The campaign will not feature Oliver, who will bow out with a farewell Christmas television campaign, as revealed in July.
The change away from "try something new today" takes the supermarket back to its roots, according to Harrrison-Church.
"We are in a much different place as a brand and our customers are in a different place and we really want to get back on focusing all the good things Sainsbury's has always stood for, which is great quality food at great prices."
The "live well for less" strapline is accompanied by a multi-million pound investment in the core own brand, 'by Sainsbury's', which will see 65% of the line-up receive a revamp by 2013.
Sainsbury's says its "by Sainsbury's" core range is its biggest own brand range by "a country mile" when compared to its other "Basics", "Be good to yourself" and "Taste the difference" own brand ranges.
The supermarket also believes it can compete with Tesco and Asda in terms of price and is setting out to prove this with a Brand Match initiative it is running in Northern Ireland.
Harrison-Church explained: "We believe we are the same price as Tesco and Asda on branded goods, if we are not we will give customers a coupon on the difference there and then at the till.
"It's entirely down to our coupon at till technology, which can instantly compare the prices. If we are cheaper we will print a coupon telling them how much cheaper we were."
Despite the supermarket's belief in its ability to match Tesco and Asda prices, it has not yet committed to rolling out the Brand Match initiative to the rest of Britain.