Otago change manager Jeremy Curragh said recently the union had to reduce player costs by $290,000 through their deal to stave off liquidation and were looking to move on players who were not keen to stay.
The 28-year-old Atiga, who made one World Cup appearance, against Tonga in 2003, signed for Otago last year but was looking to reignite his career after not making the Highlanders this year.
Edinburgh are preparing for a Heineken Cup semifinal against Ulster later this month - the first time a Scottish team has reached the last four - and coach Michael Bradley has added Atiga to provide more firepower to his squad.
"Ben has proven his ability on some of the toughest stages in world rugby and will be a formidable option at centre and fullback for at least the next two seasons,'' Bradley told the Scotsman.
"He's a very impressive package of agility, power and skill and I believe he'll make a big impact, both from a performance perspective but also in bringing on the many talented young players we have at the club.''
The Otago Daily Times reported that half a dozen other players had gone from Otago's 27-strong squad named late last year.
