"The Bundesbank board and its member Thilo Sarrazin are aware of their responsibilities to the institution of the Bundesbank," the central bank said in a surprise statement posted on its website. “Given the public debate, the parties concerned are going, of mutual accord, to end their cooperation at the end of the month.”
The Frankfurt-based Bundesbank had previously requested that German President Christian Wulff fire Sarrazin because he had refused to go quietly.
But on Thursday the bank said it had "withdrawn its request" and that the 65-year-old had asked Wulff to relieve him of his duties. The statement also thanked Sarrazin "for the work he has done."
The furore followed the publication of a new book by Sarrazin, Deutschland schafft sich ab - Wie wir unser Land aufs Spiel setzen, or “Abolishing Germany - How we're putting our country at jeopardy.”
In the book, he says Europe's top economy is being undermined, overwhelmed and made "more stupid" by poorly educated, fast-breeding, badly integrated and unproductive Muslim immigrants and their offspring.
"If I want to hear the muezzin's call to prayer, then I'll go to the Orient," he says in the book, saying that allowing in millions of "guest workers" in the 1960s and 1970s was a "gigantic error."
He also says that Turkish and Kurdish "clans" have a "long tradition of inbreeding," leading to higher rates of birth defects, and ponders whether this might be one reason for immigrants' poor school performance.
He also told a newspaper that "all Jews share a certain gene," a property he said was shared by the Basques.
Chancellor Angela Merkel called the remarks "completely unacceptable," but surveys have indicated that Sarrazin enjoys considerable sympathy among the population at large.
Backing for Sarrazin is so strong that a survey published on Sunday indicated that if he set up his own new political party, almost one in five (18 percent) would vote for him.
Sarrazin has no intention of starting a political party, but the survey raised fears that a charismatic right-wing populist in Germany, like anti-Islam lawmaker Geert Wilders in the Netherlands, could win considerable political support.
The German government has admitted that its record on integrating immigrants into society has been less than perfect.
According to official figures, nearly one in five young people without German nationality, which many second and third generation immigrants do not have, leave school with no qualifications.
Other figures show that people in Germany of Turkish origin, who number around three million and make up the largest minority, are significantly more likely to live below the poverty line.
This week, the government published a national integration programme with a focus on improving immigrants' German language skills.