Day, 30, has inked a one-year deal and comes off a 10-year career in the Pro12 (Europe), England Premiership and Top League (Japan).
Day, who made three international appearances for Wales last year and has more than 200 games of professional experience, will join the Rebels after the end of the Top League season in the new year.
"Dom is an experienced lock and an accomplished line-out caller who brings a physical presence to his game," Rebels head coach Tony McGahan said.
"He has leadership qualities having captained Bath and displays the consistent behaviour and work ethic that will be well suited to our club."
The signing comes two weeks after Rebels coach Tony McGahan signed Tongan-born Japan Test No 8 Amanaki Mafi to a one-year deal.
The Rebels finished third in the Australian conference this season with a 7-8 won-lost record and did not qualify for the playoffs.