The 26-year-old, who was part of England's failed World Cup campaign in Brazil, sealed a reported £25m transfer to Anfield on Tuesday.
Mellor, who is friends with the midfielder, is confident that Lallana will prove to be worth his price tag in a Liverpool shirt.
"He's absolutely buzzing and can't wait to play for Liverpool," Mellor told the club's official website. "He's a fantastic player. Obviously he's cost a lot of money but I think he can justify that price tag with the season he has just had and what a player he has been for Southampton.
"Many times in the past he could have left Southampton, but he's been so loyal to them and it's come to the point where an offer came in from a club in the Champions League and with it being Liverpool he was never going to turn that down. He is really excited by that and he can't wait to play in front of the Kop."