The Polish keeper has signed a one-year deal at St Mary's Stadium after his release from Serie A club Fiorentina in the summer.
Boruc told the club's official website: "I'm looking forward to playing in the best league in the world while I'm playing here at Southampton.
"I missed football, so I'm really glad that I'm here and I've finally found the club I was looking for."
"My dreams are coming true," he added of the opportunity to play in England.
"I've been talking about this for a long time, and finally I'm here in the Premier League. We'll see what's going to happen over the next couple of weeks.
"I'll give 100% and try to get in goal for Southampton. I like challenges and I'm an ambitious guy, so that'll be good for everybody."
Paulo Gazzaniga featured in goal for the Saints in their 4-1 win over Aston Villa on Saturday after Kelvin Davis had made an uncertain start to the campaign.
Southampton boss Nigel Adkins was delighted with the Argentine's performance against the Villans but was especially pleased to have added a goalkeeper of Boruc's standing to his side.
He added: "Artur has great experience from Celtic and Fiorentina, and from playing from the national team in Poland.
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"He now gives us a third goalkeeper in the building, which is important because the potential for injuries and people getting sent off means we have to cover ourselves. He gives us great back-up and competition.
"Paulo is a very young goalkeeper and he did ever-so-well for us today, and everyone knows how much I rate Kelvin – what a great character he is and how important he's been in what we've done here at Southampton.
"Artur now comes in as a third goalkeeper with a vast amount of experience."