The 27-year-old Portugal international has signed a four-year contract and will add weight to a Reds midfield which was looking short on numbers following the departures of Mascherano and Alberto Aquilani.
'Roy Hodgson was key to me coming here because he worked so hard to sign me," Meireles said in the Sunday Express.
"I am Meireles and not Mascherano and that will be clear to the fans. I hope one day the Liverpool fans will remember me for being successful."
Meireles has won four titles with Porto and been capped 38 times by Portugal, playing in all four of his country's games at this summer's World Cup.