The 28 year-old South Africa international has signed the deal but his release date is yet to be confirmed. His current contract with the Bulls is due to expire in October.
Kirchner will be seen as a direct replacement for Leinster veteran Isa Nacewa who is retiring and returning to his native New Zealand.
Bulls coach Frans Ludeke says they tried their best to keep the player, but could not compete with the Euro exchange rate and the expectations of Kirchner and his agent.
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