The Anfield outfit agreed a £67 million ($87m) deal with Roma to land the Brazil international after opening talks earlier in the week.
Alisson was thought to be open to a move to the Premier League club, though personal terms and a medical still had to be finalised.
And while nothing formal has been announced yet, the goalkeeper himself has now delivered a clear signal of his intentions, thanking Roma fans while at Ciampino Airport in Rome, and declaring it the right moment to move on.
“I want say thanks to AS Roma fans,” Alisson said. “Now it's time for a new adventure."
It is expected Alisson will arrive in Liverpool this evening.
The 25-year-old goalkeeper broke through in 2017-18, having joined the club the previous season.
After failing to feature in Serie A with Roma in his debut season after his move from Brazilian first division side Internacional in 2016, Alisson went on to play in 37 league matches this campaign, drawing interest for his strong performances.
Roma finished third in Serie A and made a memorable run to the Champions League semi-finals, stunning Barcelona with a comeback in the quarter-finals before going out to Alisson’s new club, Liverpool, in the semis.
Alisson also was Brazil’s starter in goal for the World Cup, with the nation going out in the quarter-finals to Belgium despite being one of the pre-tournament favourites.
If the move is completed, it will be a record-fee for a goalkeeper.