The sale is conditional to shareholder and authority agreement and the move comes just days after a proposed merger between Boots and Alliance UniChem.
The sale price is higher than expected and Boots intends to return about£1.43 billion of the sale proceeds to shareholders.
Retail analysts commented that the BHI sale price was 'top of the range' and Boots chief executive Richard Baker said: 'Together with the announcement of the proposed merger with Alliance UniChem, this disposal allows us to focus on our plans to create a world-class pharmacy-led healthcare group.'
Reckitt, an Anglo-Dutch household products group, is said to have beaten competition for BHI from Bayer, Novartis and GlaxoSmithKline.
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