The 28-year-old was a free agent after leaving Premier League champions Chelsea last month and had been linked with moves to Tottenham Hotspur, Arsenal and Manchester United.
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Given that those three clubs will all be featuring in this season’s Champions League, it came as a surprise that Cole should leave his native London for a club who will be playing in the Europa League, not that it concerned Hodgson.
"I'm very pleased because any concern that it was going to turn into an auction all about money quickly disappeared after myself and Christian Purslow had a long conversation with Joe," said Hodgson.
"Obviously he is going to be a high wage earner because he is a free transfer - he was at his previous club - and he would be worth a lot of money on the transfer market.
"We wanted to make it clear that we wanted him for football reasons and only if he fitted in with our wage structure. 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."
Liverpool were the only club to reportedly match his £90,000-per-week salary demands but Hodgson thinks the England international is worth every penny.
"He's one of the best attacking midfield players in England. He's a player that can play in a number of attacking positions, which is very useful," Hodgson said.
"He's a quality player. He has an all-round quality that makes him a good player and one we hope we can get a lot of use out of this year."
The Reds have handed Cole the number 10 shirt ahead of the Premier League curtain-raiser in three-weeks.
By James Martini
