Alisson sent a message to Roma and Liverpool fans before he boarded the plane to the UK to undergo a medical.
The Brazil number one spoke out before making his way to Merseyside, after agreeing personal terms on a five-year contract.
The Reds submitted a £66.8million bid for the highly-rated Roma shot-stopper, which would make him the most expensive goalkeeper in world football history.
Alisson left Ciampino Airport on Wednesday - the same day Liverpool's bid was accepted by the Italian club.
Before the 25-year-old departed he was met by members of the press and told ForzaRoma: "I want to say thanks to Roma fans. Now it's time for a new adventure."
The keeper cut short his holiday in Sardinia to complete the medical formalities before he is set to become the most expensive goalkeeper in the world.
An official announcement is expected to come either today or tomorrow.
Alisson is unlikely to be part of Jurgen Klopp 's squad for the pre-season tour of America as he's given time off following his exertions at the World Cup.
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However, he should link up with his new team-mates for the four-day training camp in France ahead of the friendly against Napoli in Dublin on August 4.
Liverpool agree Alisson deal
Liverpool's initial bid of £62million was rejected by the Serie A outfit but sporting director Michael Edwards moved quickly to reach an agreement.
Including add-ons, the deal is understood to be worth 75million Euros (£66.8million). That shatters the previous highest transfer fee involving a goalkeeper – the £34.7million that Manchester City paid Benfica for Ederson in 2017.
The Reds have been wary of Chelsea's interest potentially scuppering the transfer but it would now take a dramatic late twist for Klopp to be denied his top keeper target.
Alisson, who was blown away by the Anfield atmosphere when he played for Roma in the Champions League semi-final last season, is excited about the opportunity to play for Klopp. He has also received a ringing endorsement about life at Liverpool from Brazil team-mate Roberto Firmino.
Liverpool have been in the market for a new No 1 since the midway point of last season. Loris Karius' disastrous performance in the Champions League final only strengthened their resolve to bolster that area of the squad with proven quality.
The Reds initially feared they would miss out on Alisson with Real Madrid seemingly favourites to sign him but the landscape has changed in recent weeks with the Roma No 1 increasingly keen on the prospect of moving to Anfield.