The 28-year-old has opted to move to Ireland rather than extend his contract with the South African Bulls franchise beyond its expiry at the end of October.
It is unclear when Kirchner will join his new team, with Bulls high performance manager Xander Janse van Rensburg hinting that the player could request a release before his current deal ends.
"We understand that an earlier release might be requested, but it is up to the board to approve that or not," Van Rensburg said in a media statement release by the franchise on Monday
"We have been in talks with Zane and his agent since November and although it is very disappointing to lose his services, we wish him well."
Kirchner joined the Bulls franchise in 2007 from Currie Cup side Griquas and was part of the squads that won the Super Rugby competition in his first year, and later in 2009 and 2010.
He made his Springbok debut in 2009 and has made 24 appearances.