As transfer deadline day came to a close, Liverpool confirmed that Meireles had handed in a transfer request at Anfield.
The 28-year-old was thought to be the subject of a bid from Chelsea earlier in the week and the London club subsequently confirmed that they had signed the midfielder on a four-year deal.
The Blues had been hoping Meireles, who signed a four-year deal, would be joined at Stamford Bridge by Porto left-back Alvaro Pereira but they were unable to reach an agreement before the 11pm deadline.
New signing Ulises Davila also joined Vitesse Arnhem for the season.
Meanwhile the Merseysiders confirmed that Bellamy has returned to the club on a free transfer having signed a contract, although they have not released any further details regarding the deal.
City have been desperate to offload Bellamy but with a year left on his contract there were financial issues to sort out before Liverpool could complete a deal.
In a brief statement the club said: "Liverpool have tonight announced Craig Bellamy has signed a contract with the club. He will wear shirt number 39."
"I've grown up with Kenny Dalglish, now to be signed by him is a massive honour," he said. "This is an exciting time. When Kenny took over, watching as a fan last season I got the buzz as well and it was great to see Liverpool end the season well.
"To every Liverpool fan, Kenny is probably the best player ever to pull on the red shirt so that speaks for itself. He was the first player-manager to do the Double and just how he conducted himself really (made a difference).
"I know we've had bits of success since then but the club hasn't been the same since he left, so to come back in and be a part of this with the players who are here - it's a good time."