The former Liverpool star believes the England striker will prove himself to be worth his €5 million transfer fee by providing worthy back-up to Daniel Sturridge and Luis Suarez
The England international striker, who is currently preparing for the upcoming World Cup, became Brendan Rodgers' first signing of the transfer window earlier this week, ending his successful five-year stint at Southampton.
Lambert, a boyhood Liverpool fan, scored 13 Premier League goals last season and bolsters a forward line that already boasts Luis Suarez and Daniel Sturridge, who scored over 50 league goals between them in 2013-14.
Former centre-back Carragher, who made over 500 appearances for the Reds, thinks that Lambert will be a good compliment to Rodgers' attacking options.
"I think it's a very good signing," Carragher told Liverpool's official website.
"He's a local boy, a Liverpool fan, and it's probably been a dream for him.
"There'll be lots of games with Liverpool being involved in the Champions League, so he'll play his part and I'm sure he'll get some goals."
Lambert joins a Liverpool contingent that includes Sturridge, Steven Gerrard, Raheem Sterling, Jordan Henderson and Glen Johnson in England's 23-man squad for the World Cup, with the former Bristol Rovers man among the scorers in Wednesday's 2-2 draw with Ecuador in Miami.
Carragher hopes all of Liverpool's England players can all excel in Brazil, as well as Suarez, who could line up against England for Uruguay.
He added: "I'm eager for them all to do well - also Suarez, who is playing against England, so that'll be difficult.
"I think England will qualify from the group and then who knows who they'll get in the draw."
Lambert will soon be joined at Anfield by Emre Can, with Liverpool agreeing a deal to sign the Bayer Leverkusen midfielder on Thursday.