Kydd, who is EU qualified, has represented New Zealand at various levels, as well as being an integral part of the New Zealand Universities side last season.
The 21-year-old, who can play fly-half or centre, has been a member of the Otago Highlanders Super 12 Development squad for the last two seasons, also playing for the U23 team when only 19.
"Robbie is a young talented player who is joining us initially on a short-term contract," said Bath head coach John Connolly.
"He is someone that we very much intend to develop as a Bath player of the future. He has thus far in his career shown outstanding potential and has played some quality rugby in New Zealand with the representative teams and also as a part of the Otago Highlanders Development squad."
"I'm really pleased to be here," said Kydd after his flight over from New Zealand.
"It's a real honour to have signed for a club like Bath, they're famous throughout the world of rugby and have such a great reputation. I'm really looking forward to playing with guys like Mike Catt and Mike Tindall."
