"We have a number of injuries out wide at the moment," said Connolly. "Therefore, it was necessary to bring in another wing.
"We're delighted to sign someone of Salesi's quality and experience.
"He had a great record with the Scarlets, for whom he made a big impact and we are looking forward to seeing him in action here."
After nearly seven years at Stradey Park, the former rugby league star will spend the rest of the season with the English side, putting his return to Australia on hold.
"It has all come about very quickly for me," said Finau. "I had a great time with the Scarlets, but the opportunity of playing with Bath is a fantastic one.
"They are one of the top clubs in England with a proud tradition and I am looking forward to making a contribution."