The Giants announced the move on their official Twitter feed on Wednesday morning, adding that the 25-year-old Tonga international has signed a three-year contract at the Galpharm Stadium.
A second or front-rower, Ta'ai has been with the Warriors since 2009 but was told midway through this season that he would be released for 2013.
Ta'ai is Huddersfield`s third signing for 2013, adding to Anthony Mullally and the already-joined Brett Ferres.
"Ukama has been on the Giants' radar for quite a while and when I heard he may be available for a UK move I earmarked him as a priority signing," said coach Paul Anderson.
"We will work out how to best utilise his skills during pre-season."
Ta'ai added: "Huddersfield are always in the play-offs and I am excited about helping move them forward next year and will be supporting them in this year's play-offs from here at home.
"I think their style will suit my strengths as will the Super League in general so all we need do now is tie up the paperwork and plan for the move to the UK."