The 23-year-old Gabon midfielder has put pen to paper on a five-year contract with the Saints, a transfer which Juventus confirmed was worth 17m euros (£15.6m) and could increase by a further three million euros (£2.77m).
Lemina helped the Bianconeri win the Serie A title as well as reach last season's Champions League final against Real Madrid, and had been linked with a number of clubs before completing his switch to St Mary's Stadium under new manager Mauricio Pellegrino.
Saints kick off the new Premier League campaign at home to Swansea on Saturday, and Lemina hopes to be able to hit the ground running.
"I think I can bring to this squad, whether it be offensively or defensively, my power and ability to defend and get things moving forwards. In that way, I can give my very best for the team," he said in an interview with Southampton's You Tube channel.
"I have a lot of friends from France who are here and have explained to me what it is like to play in the Premier League.
"I know the Premier league is a different league and I hope that I can adapt quickly to it because I know that it is a league where everything goes quickly."
Lemina added: "The aims are the same as they were last season - to finish high up the table, whether that be sixth, seventh or eighth. Why not challenge for the Europa League?
"As I have seen, the club is very ambitious and we want to stay on this upward path".
Lemina started his career in France with Lorient before joining Marseille in 2013 and initially signing on loan with Juventus in 2015, ahead of completing a permanent transfer last summer.