The Fiji-born back, 30, has accumulated over a century of appearances in Super Rugby for the Brumbies and has appeared for his country 19 times.
Speight has agreed a short-term contract with Ulster that runs until 31 December and revealed he was persuaded to make the switch after speaking to Brumbies team-mate Christian Lealiifano about his time in Belfast.
"I'm excited to have the opportunity to represent a big club like Ulster," Speight said.
"I've spoken to Christian a lot regarding this move and he had only great things to say about the staff, players, supporters and wider community, which welcomed him with open arms.
"This is a fresh challenge for me and I hope to embrace it by relishing every moment and by adding value to the group as best I can. I can't wait to arrive in Belfast and get to work with my new team-mates."