Having seen Simon Mignolet and Loris Karius fail to convince in 2017-18, Jurgen Klopp made the signing of a new goalkeeper a top priority for the summer transfer window.
He was forced to dig deep in order to bring a proven No. 1 on board, but finally got his man when tempting Roma into parting with Alisson.
The South American is relatively short on top-level experience despite his price tag, but Grobbelaar believes the 25-year-old will prove his worth over time.
The former Reds keeper told the Mirror: “Anyone who comes out of Brazil at a young age and comes over to Europe has got to have a big heart and a big personality.
“He has that in abundance and he will go from strength to strength in the Premier League. He's a great buy - even at that money.
“With Roma he was fantastic and has learned his trade in Europe. Now this is an even bigger challenge in the Premier League at Liverpool but he's made for it.
“He has played at the high level for Brazil in the Wold Cup and Roma in Serie A. He won't have a problem at all.”
Liverpool, having signed Virgil van Dijk in January, hope to have plugged the defensive leaks which held them back at times last season.
Grobbelaar feels they are now better placed to challenge for top honours, with Alisson set to slot seamlessly into the fold between the sticks.
A man who won six league titles and the European Cup during his time on Merseyside added: “It can be daunting playing in front of the Kop. But when Roma were at Liverpool last season in the Champions League semi-finals he [Alisson] saw what kind of atmosphere is generated at Anfield.
“He embraced that and wanted more and that's a good sign. It'll be a dream for him to come and have that every other week."
“He is the keeper Jurgen has pinpointed and we got him. And I believe he will make a big difference.”
Liverpool are set to open their 2018-19 campaign at home to West Ham on Sunday.