£6.8bn takeover deal for Leeds-based Asda agreed
Walmart will retain a minority stake in Asda as part of the agreement.
The new owners have committed to keeping the retailer's headquarters in Leeds and has said it will invest to grow its convenience and online operations.
It comes more than a year after a proposed merger between Asda and UK supermarket rival Sainsbury's was torpedoed by regulators.
Asda has seen its fortunes improve recently with trading strengthening through 2020, as shoppers have spent more money on groceries during the pandemic.
In the quarter to June, Asda saw online sales double but the new owners will be tasked with expanding its digital business further to take advantage of soaring demand and make ground on rivals, such as Tesco, who have a larger slice of the market.
The new owners will also face the challenge of keeping prices low amid tough economic conditions for shoppers and potential new tariffs on EU-imported foods, with the other big four supermarkets all announcing a raft of price cuts in recent months.
EG Group has sealed the deal after its offer was favoured by Walmart ahead of a move by US private equity firm Apollo.
Last week, a third bid from Lone Star Funds, fronted by former Asda executive Paul Mason, was dropped after failing to meet the price of its rivals during the latter stage of bidding.
Walmart sought a sale after the UK's competition regulator blocked its merger with Sainsbury's amid fears the move would push up prices and reduce product quality.
The US grocery started new discussions over a sale of Asda in February, but saw these halted due to disruption as a result of the coronavirus pandemic.
However, the auction process restarted in July as Walmart sought to exit the UK, 21 years after first purchasing the Leeds-based retailer.
Blackburn-based EG Group, formerly known as Euro Garages, already runs forecourt convenience stores for Spar and French hypermarket chain Carrefour.
The deal will have to pass through regulators, although it is expected to be given the green light.
Last week, EG Group announced a trial involving three "Asda on the Move" convenience stores at its petrol forecourts.
TDR Capital, which also owns the UK's largest pub group Stonegate, owns a 50 per cent stake in EG Group, sharing ownership with the Issa brothers.