The England midfielder has agreed personal terms with the Reds and will undergo a medical in the next 48 hours.
Cole becomes the club's second signing of the summer after Milan Jovanovic.
The 28-year-old arrives from Chelsea, where he won three league titles and two FA Cups during a seven-year spell.
He is a product of the West Ham youth system and has represented his country 56 times, scoring 10 goals in the process.
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