The new group, Walgreen Boots Alliance, will be based in Chicago but the headquarters of Boots will remain in Nottingham. Walgreens said a programme of cost-cutting would target one billion US dollars (£594 million) in savings by 2017.
Alliance Boots employs more than 108,000 staff in more than 25 countries, including 70,000 in the UK, where Boots has nearly 2,500 stores.
Walgreens bought a 45 per cent stake in Alliance Boots for 6.7 billion US dollars (£4 billion) in 2012, with the option to buy the rest by August 2015.
But the announcement means it will complete its take-up of the 55 per cent remainder by February, in exchange for just over £3 billion in cash plus 144.3 million shares - with a value of just under £6 billion.
It brings the total value of the deal to around £9 billion, meaning Walgreens has spent about £13 billion acquiring Alliance Boots - which comprises both Boots the Chemist and pharmaceuticals distribution arm Alliance.
The latest transaction will reportedly net a £1.5 billion windfall for executive chairman Stefano Pessina, who took Alliance Boots private, with private equity firm KKR, in an £11.1 billion deal in 2007.