The 26-year-old on Wednesday passed his medical to complete a £1.75million switch from Middlesbrough on a three-year contract.
Lita has previous Premier League experience from his time at Reading, where he impressed during the Royals' two-season stint, but he has not played in the top tier since their relegation in 2007.
And he is keen to take his chance with Brendan Rodgers' side.
He told the Swansea website: "It's something I have been looking forward to for the last week so to finally be here is a great feeling and I can't wait to get started.
"I always believed in myself and now I am here and I know there are good players here. We have a great squad and hopefully we can really push on this year and surprise a few people.
"I have been waiting for this chance for a while and I am looking forward to getting back to that level.
"This is a new challenge for everyone and they (Swansea) deserve to be here.
"They have been playing the best football outside the Premier League for a number of years so it's only fair they get their chance and let's hope we can push on."
Lita missed out on playing for current Swans boss Rodgers, as he left the Madejski Stadium shortly after the Northern Irishman's arrival in 2009.
But he has been impressed by Swansea's style of play over recent seasons and says his team-mates have given him nothing but positive impressions of his new boss.
"I never played under him but I spoke to a few of the lads and they love playing under him and it makes you feel at home and makes you enjoy your football," he said.
"I am looking forward to getting to starting to work with the gaffer, the staff and the boys.
"Swansea were one of the fixtures you didn't like as a striker because you knew you wouldn't see much of the ball. You seemed to be chasing all the time and it's nice to be a part of it and hopefully we can take that into the Premier League."
On the evening he signed, Lita made his debut off the bench in a 2-0 friendly win over Celtic at the Liberty Stadium.
And Rodgers was pleased by what he had seen.
"I am delighted to have signed Leroy," he said. "He is a great addition to the group. He has blended in well and just wants to play.
"He went through the stringent medical process that we have here and he completed that and jumped out to play tonight without a training session.
"Tonight I think you saw his strength, and his movement and pace threatened in behind. I believe he will be a great addition to this group over the next few years."
Lita is Swansea's fourth summer arrival, and is the second striker to be added to the Swans' ranks following the capture of club record signing Danny Graham from Watford for £3.5million.
He will also compete with Craig Beattie and Luke Moore for a starting role when the Welsh side open their maiden Premier League campaign at Manchester City on August 15.
Swansea are also closing in on completing a deal for Newcastle winger Wayne Routledge.
A fee has been agreed for the former England Under-21 international, but it is understood he is likely to be confirmed as a Swansea player on Thursday, taking up a three-year deal, once he completes his own medical.