Liverpool have completed the signing of Joe Cole on a four-year contract after the midfielder passed his medical.
The 28-year-old agreed personal terms on Monday after being released by Chelsea at the end of last season and then flew to the club's training camp in Switzerland to undergo his physical examination.
Contrary to reports, the England international has been allocated the number 10 shirt.
Liverpool sprang something of a surprise when they won the race for Cole as it was expected he would remain in London with both Arsenal and Tottenham interested.
Much was made of his reported £90,000-a-week wage demands but Hodgson was prepared to pay up as he believed Cole has chosen the club for football rather than financial reasons.
"We wanted to make it clear that we wanted him for football reasons and only if he fitted in with our wage structure," the Liverpool boss said on Tuesday.
"I'm pleased to say that Joe has chosen Liverpool to come and play football - and not because of the money.
"That's a very satisfying thing for me as a manager and for the club itself."