The defending Stanley Cup champions announced the deal on their Twitter account Monday, saying the trade is contingent on Regehr passing a medical exam.
In exchange, the Sabres acquired the Kings second-round picks in 2014 and 2015.
The 13-year NHL veteran will be an unrestricted free agent this summer, and waived his no-trade clause to approve the deal.
He has two assists in 29 games this season, but Los Angeles covets Regehr's physical defensive play while defencemen Matt Greene and Willie Mitchell remain out with long-term injuries.
Regehr spent the past two seasons with Buffalo after 11 seasons with Calgary, where he played for Kings coach Darryl Sutter.