The 21-year-old arrives at Welford Road as an injury dispensation signing with Matt Smith ruled out with a thumb injury.
Hepetema, who was born in England, qualifies to play for Australia and New Zealand through his parents. He moves to Welford Road from the New South Wales Waratahs in Australia.
Tigers director of rugby Richard Cockerill said: “We’ve got good competition right through the squad but an opportunity has arisen to bring Terrence in.
“He can play at inside or outside centre and adds to the squad as we go into the new Aviva Premiership season.
“He spent some time with the Waratahs towards the end of last season and we are looking forward to seeing how he develops.”
Hepetema made his Super 15 debut for the Waratahs against Western Force last season. He was selected for the Australia Under-20s training squad in 2012 ahead of the IRB World Junior Championship.
Hepetema said: “It’s awesome to be here, I’m loving it.
“The boys have been really good. The training is excellent and I can feel myself getting better already.
“Geordan Murphy has been awesome, helping me out.
“I want to keep my head down and work hard. There are a lot of games during the season and I have to earn my stripes.
“I am going to do whatever I can to push for a place and, hopefully, me working hard can push the other boys.”