The Reds shelled out a world-record fee for a goalkeeper in capturing the Brazil international from Roma for £65million earlier in July.
He has now joined Jurgen Klopp’s men at their training base in France following a post-World Cup break.
Alisson said on liverpoolfc.com: “It has been a great day which I had been looking forward to.
“I’ve had a good few resting days with my family but we all couldn’t wait to get the new season under way soon. It’s only my first day and I feel at home already.”
Alisson’s Brazil team-mate Roberto Firmino also reported back for training, and the pair could play a part in Liverpool’s two remaining pre-season matches, against Napoli on Saturday and Torino next Tuesday.
The Reds then begin their Premier League campaign against West Ham on August 12, and Alisson said: “Although these two weeks don’t seem like a long time, it’s enough for us to be ready for our first game against West Ham.
“We’ll play two friendlies before this game and I’m sure the hard work the squad have put in so far is going to help me become a member of the squad as quickly as possible so that I am 100 per cent ready for our first game to kick off the Premier League in a good way.
“My first impression tells me it won’t be difficult for me here – it’s a great squad formed by great players and brilliant professionals. I’m sure it’s going to be a great season for us all.”
Xherdan Shaqiri’s former team-mate Charlie Adam has warned Liverpool over the Switzerland international’s attitude.
Shaqiri, who played alongside Adam for Stoke last season as they were relegated from the Premier League, joined Liverpool this summer and marked his debut by scoring a superb overhead kick in a 4-1 pre-season victory over Manchester United.
Adam described Shaqiri as a “top player”, who deserved to be at a club of Liverpool’s stature, but questioned his commitment at crucial times in Stoke’s relegation fight.
“He’s a big player, at times he did well for us,” Adam said on the BBC Sport website.
“But in critical situations, I felt tracking back and what we needed for the team in a relegation battle just wasn’t there.
“He has got it in him, but he probably knew we were going to get relegated, he was going to the World Cup and had this big move – this move was probably done three, four months ago.
“He is a match-winner, but at times it was difficult to play in the same team. The manager would let him get away with certain things.”
Adam said Shaqiri could soon start to grow impatient if he struggled to hold down a first-team place.
“He might get frustrated at not playing as much as he wants – it’s how long he waits and what (manager Jurgen) Klopp does with him,” the Scot added.
Liverpool have announced their female team has been renamed and will now be known as Liverpool FC Women.
The side, previously known as Liverpool Ladies FC, last season came sixth in the Women’s Super League, a competition they won in 2013 and 2014.
A statement on liverpoolfc.com on Monday said: “With the rebrand of the Women’s Super League and a fresh and exciting team under the new management of Neil Redfearn, Liverpool FC has taken the opportunity to launch Liverpool FC Women, previously known as Liverpool Ladies FC.”
Redfearn, who was appointed in June, said: “We are entering a new era for women’s football and this is an ideal time to review every aspect of our team, to ensure we are set up for future success.
“The renaming of my refreshed squad is just one aspect we’re looking at and fits perfectly with the overall move towards a more modern and inclusive game.”
— Liverpool FC Women (@LFCLadies) July 30, 2018
Liverpool chief executive Peter Moore said: “I have witnessed women’s football go from strength to strength over the last few years and I’m excited about this new stage in the game.
“We are in a prime position to be at the forefront of these changes, so it was an obvious choice to rename the squad before the new season starts.”
This summer has also seen Arsenal, Chelsea and West Ham’s female sides renamed, with the word ‘Ladies’ being dropped and ‘Women’ being used.