Originally announced in November, the FTSE 250-listed industrial thread producer said will fund the transaction with operating cash flows and existing debt facilities.
Last financial year Pharr posted sales of US$110mln and adjusted underlying earnings (EBITDA) of US$5mln.
Founded in 1939, it specialises in providing technical yarn solutions to markets such as industrial thermal protection, defence and fire service.
Coats, which is the second-largest manufacturer of zips and fasteners in the world, said the acquisition adds to its personal protection business.
Shares rose 1% to 72.82p on Tuesday at the opening bell.