The Croatia international joined from Southampton for around £20 million last month, but was unable to join the Reds on their pre-season tour of the United States.
However, the former Lyon defender is expecting to play some part in the final friendly of the summer when they take on Bundesliga giants Borussia Dortmund at Anfield on Sunday.
The arrival of Lovren strengthens the defensive ranks further, and Brendan Rodgers now has plenty of options to choose from when picking his centre-backs.
The Reds have Mamadou Sakho, Daniel Agger, Lovren, Skrtel, Kolo Toure and Sebastian Coates on their books, but the Slovakian international has welcomed the arrival of the former Saints star.
Speaking to the club's official TV station, Skrtel said: “He’s an experienced player, he played for Croatia in the World Cup and he played for Southampton last year."
"There’s [more] competition for us, because he is another centre-back and as I said I think it is only good for us as players to fight for our place and have players who push you hard every single session."
“We welcome him to the team, and it’s going to be a difficult season, we need a big squad and every single player is welcome.”
The 29-year-old also gave his first impressions on new £10 million signing Emre Can, following the German's arrival from Bayer Leverkusen.
The Reds fended off competition from Bundesliga champions Bayern Munich to land Can earlier this summer, and Skrtel believes that he is a similar type of player to England international Henderson.
“He’s a similar player to Hendo you know, he is a very powerful runner," he added. "He will run all day long and he is very strong as well, so he will add to our midfield, and he’s a top guy."
"He's also a top footballer and he fits into the team well. He will be a great player for Liverpool this season and he has a lot of years to play."
Lovren and Can are just two of seven new additions at Anfield this summer. The pair arrived for a combined £30 million, and a further £60 million has been spent on the likes of Adam Lallana, Rickie Lambert, Lazar Markovic, Divock Origi and Javier Manquillo.
Atletico Madrid right-back Manquillo arrives on a two-year loan with the option to make the deal permanent for £5 million, while Belgium international striker Origi will stay on loan with Lille for the coming season after his £10 million switch.