The 32-year-old has signed a two-and-a-half-year contract with the Scottish champion and will officially join up with the squad when the transfer window opens in January.
"The last half-a-year, I wasn't playing so much at Leipzig," he told CelticTV after finalising the deal.
"The recruiting staff were looking for an experienced defender. They made contact with my agent and I'm very glad to be here."
The centre-back, who started his senior career with Borussia Monchengladbach, joined Leipzig in 2014 after spending a season with Fiorentina.
He played 25 times in the Bundesliga last season but has found his role limited in 2017-2018, managing just two appearances in the league and one in the UEFA Champions League.