Under the proposed deal, Albertsons shareholders would own roughly 71% of the combined company while Rite Aid investors will own the rest.
If approved, the acquisition would create a company with revenue of US$83bn.
It would also pave the way for Albertsons to go public after more than 10 years of ownership by private equity firm Cerberus Capital Management LP.
The deal comes after federal regulators blocked the full sale of Rite Aid to Walgreens. Rite Aid now plans to sell 1,932 stores to Walgreens.
Rite Aid’s revenues have been hit by a slowdown in branded drug price rises and a drop in reimbursement rates for generics.
Amazon has become a new rival in food retail following the purchase of Whole Foods Market Inc while Walmart has improved its e-commerce offerings and product ranges.
“We know that scale matters,” Albertsons chief executive, Bob Miller, told the WSJ. “We continue to grow to compete with all competitors, not just Amazon.”