The Croatia international became the third player to leave Southampton for Liverpool during the transfer window, following the paths previously trodden by Rickie Lambert and Adam Lallana.
Lovren's move was the subject of much media speculation, with the defender publicly declaring his intention to leave Southampton last month.
The 25-year-old got his wish in late July and ahead of Sunday's opening Premier League clash against his former club, Lovren claimed he had options to move elsewhere.
"I had better offers financially but from the first day I said I want to come to Liverpool," he said.
"I want to achieve something here because I know this club is big and Brendan Rodgers is a great manager.
"There is a lot of talent here - amazing players - and last season they showed they can do something. I'm really confident in this team."
Lovren scored the winner for Southampton in a 1-0 victory in the corresponding fixture last season, and insists he is focussed solely on the job at hand.
"To play them in the first game was destiny," Lovren said.
"I will just have to concentrate on my game, on our style and I won't think about Southampton.
"Maybe there is some regret with how I left Southampton. I said that I wanted to leave because Liverpool is a massive club and maybe I will have this chance just one time in my life.
"It was not so easy at the beginning. It took a lot of time. But at the end everybody agreed and I shook their hands and said goodbye so now it is finished."