Liverpool agreed to pay Andy Carroll in excess of £1million to pave the way for his Anfield exit.
The England striker joined West Ham in a £15.5m switch earlier this week despite interest from former club Newcastle.
Carroll has signed a six-year deal at Upton Park following a season-long loan spell but only after weeks of deliberation.
Liverpool were so keen to free up some of their budget for new arrivals that they offered Carroll the money to supplement his £100,000-a-week wages.
Carroll's move represents a £19.5m loss for Liverpool after they paid Newcastle £35m for his services in January 2010.
He scored 11 goals in 58 games for the Reds but Brendan Rodgers made it clear that he did not feature in his plans when he took over at Anfield last summer.
The nine-cap England international, 24, netted seven goals in 24 games on loan at Upton Park last season.