The American retailer, which also trades as Duane Reade, is expected to spend about £5 billion on the outstanding 55% stake in Alliance Boots, which comprises Boots the Chemist and pharmaceuticals distribution arm Alliance.
An announcement is expected later today, with Sky News also reporting that Walgreens will shun the opportunity to move its corporate headquarters to the UK or Switzerland, where it can pay less tax.
Walgreens acquired its 45% stake in Alliance Boots for 6.7 billion US dollars (£4 billion) in 2012 and has the option to buy the rest by next August. The deal for full ownership of the business is expected to be completed in 2015.
Alliance Boots is also owned by executive chairman Stefano Pessina and private equity firm KKR after they took the Nottingham-based business private following an £11.1 billion deal in 2007.
Walgreens trades from more than 8,500 locations across the US, while Alliance Boots has 2,500 stores and approximately 75,000 staff in the UK.
Boots brands such as No7 and Botanics are already sold in Walgreens and Duane Reade stores in the US, with the American firm's products introduced to Boots stores as part of the deal in 2012.
Alliance Boots traces its roots back to 1849 when John Boot opened his first store selling herbal remedies in Goose Gate, Nottingham. It opened its 1,000th store in 1933 followed by the No7 cosmetics range two years later.
Boots Group merged with Alliance UniChem to form Alliance Boots in 2006 before it was taken private in Europe's largest leveraged buyout a year later.