He will join his younger brother, All Blacks back Charles Piutau, who is already with the Midlands matchday-based club until the end of the season.
Wasps boss Dai Young has signed Piutau, 30, as cover for injured trio Alapati Leiua, Andrea Masi and Ben Jacobs.
In addition, Elliot Daly is on standby for England bench duty in Saturday's Six Nations opener at Murrayfield.
"We've been left a little bit short with injuries in the centres," said Young. "We're expecting Ben Jacobs to be back fit in the next few weeks but, with Elliot away on England duty, we needed to add a bit of depth.
"Siale's transition into the squad will no doubt be made slightly easier by having his brother here."
Wasps stand fifth in the Premiership, eight points adrift of the top four, going into Saturday's home game (14:00 GMT) with struggling Newcastle, when old boy Andy Goode is likely to make his return to the Ricoh Arena.
The Piutau brothers were both born in New Zealand, in Auckland, but Siale chose to represent Tonga, winning the first of his 24 caps in 2011.
Younger brother Charles, 24, who is already contracted to Ulster for the 2016-17 season, opted to take up the offer of a one-season deal with Wasps after being left out of New Zealand's ultimately victorious Rugby World Cup squad.
Piutau Sr did play at the World Cup, playing all four group games against Georgia, Namibia, Argentina and New Zealand.
Wasps have signed Tonga centre Siale Piutau for the rest of the season from Japanese club Yamaha Jubilo.