The new scheme from Amazon Fresh, which delivers groceries to Amazon Prime members, will match its prices to Tesco Clubcard deals on everyday items, including meat and fish.
"We know that our customers are looking for ways to save on their weekly grocery shopping," Russell Jones, Amazon Fresh director said.
Facing the toughest economic conditions in decades, Britain's food retailers are monitoring each others' prices more than ever.
Tesco's Clubcard Prices scheme has been popular with consumers. Holders of the group's loyalty Clubcard pay up to a half less than non-holders across some 3,000 products both in-store and online.
When Clubcard Prices are taken into account, Tesco increasingly features as the cheapest of Britain's big four supermarkets in The Grocer's widely-followed weekly pricing survey.
Tesco and No 2 player Sainsbury's also price match products to German-owned discounter Aldi.
Amazon does not break out figures for its UK grocery sales, making it problematic to estimate its market share.
However, the Competition and Markets Authority ruled in February that Amazon must comply with the Groceries Supply Code of Practice.
The code only applies to retailers with an annual turnover of more than 1 billion pounds ($1.2 billion) in grocery sales.
Tesco has an over 27% share of the UK grocery market.
($1 = 0.8361 pounds)
(Reporting by James Davey; Editing by Kirsten Donovan)