The Schönstatt Movement said the 85-year-old Cox arrived on Sunday in the capital Santiago, where he would be available for questioning by authorities.
Read more: Pope tells predator priests to turn themselves in
"If the justice system demands it, we assure that Francisco Jose Cox is prepared to work with authorities," the Schönstatt Movement told Germany's DPA news agency. The group added that it would also work with Chilean officials if requested to do so.
Cox had spent 17 years with the Schönstatt Movement, located near the western German city of Koblenz.
Cox resigned as bishop in 1997 following accusations that he had abused young people, although he was never charged.
In October, Pope Francis expelled Cox from the Catholic Church in response to a series of abuse scandals that have rocked the Church, including in Chile.
Read more: Pope expresses 'shame' to Chileans over sexual abuse
Schönstatt Movement to work with Chilean authoritiesCox had also been suspected of sexually abusing a 17-year-old in Germany, but no criminal charges were ever filed against him.
Cox suffers from diabetes, prostate cancer and senile dementia. It was unclear if Chilean authorities will prosecute or question him.
The former bishop has been taken to a private residence outside the Chilean capital where he will be cared for.
cw/amp (AP, dpa)
Each evening at 1830 UTC, DW's editors send out a selection of the day's hard news and quality feature journalism. You can sign up to receive it directly here.