The Times reports that the former Stade Français and Swansea boss is to bolster their coaching resources, bringing into question the title and role of current co-coach, former Wallaby and Ireland fly-half Brian Smith.
Connolly has long ties with current Bath coach Michael Foley, the former Wallaby hooker who played for Connolly during his successful stint with the Reds, and joins a staff with a big Aussie influence, including skills coach Richard Graham, the former international Sevens player.
The vacant post at Irish province Leinster had been one which Connolly had been linked to, after leaving Welsh club Swansea earlier this season due to their dire financial problems.
But instead he joins an underachieving Bath side who narrowly avoided relegation last season, but have spent big in the off-season with the recruitment of stars such as England flanker Michael Lipman and Test prop David Flatman.
Others to join are Leeds' Samoan No.8 Isaac Feaunati and Gloucester lock Rob Fidler.