The March 29 letter comes after the appellate court's Judicial Council issued a March 15 order on the investigation into the February 2012 email.
The council's order will remain confidential during an appeal period, the statement said.
A Cebull aide directed calls for comment to Clerk of Court Tyler Gilman, who said Wednesday that Cebull would not have any comment other than the court's statement.
He declined to release the resignation letter or describe what it said.
Appellate Court spokesman David Madden did not return a call.
Cebull wrote a letter of apology to Obama and filed a complaint against himself after The Great Falls Tribune published the contents of the email, which included a joke about bestiality and the president's mother.
The Billings judge forwarded the email from his chambers to six other people on Feb. 20, the newspaper reported.
Two other groups also demanded an investigation, with one, the Montana Human Rights Network, starting an online petition calling for Cebull's resignation.
Kim Abbott, the network's co-director, said Wednesday she was pleased with the announcement but hopes to see the results of the investigation.
"The email really called into question his ability to treat women and people of color fairly, so we're happy Montanans will get to appear before a different judge," Abbott said.
The complaints were referred to a special committee appointed by the appellate court to investigate whether Cebull's email constituted misconduct.
Kozinski's statement said the committee submitted a report to the Judicial Council in December after "a thorough and extensive investigation" that included interviews with witnesses and Cebull and going over related documents. The council issued its order based on that report.
The statement says the Judicial Council will not comment further until Cebull's retirement is effective.
Cebull previously said he would take senior status March 18, which would have allowed another judge to be appointed while he continued working with a reduced caseload.
U.S. Sen. Max Baucus then formed a committee to replace Cebull and another judge taking senior status, with Baucus recently recommending that Obama appoint state District Judge Susan Watters of Billings to take Cebull's spot on the bench.
The new chief federal judge, U.S. District Judge Dana Christensen, plans to meet with other judges to discuss how to handle the Cebull's cases, Gilman said.
Cebull was a Billings attorney for nearly 30 years before becoming a U.S. magistrate in Great Falls in 1998.
He became a district judge in 2001 and has served as chief judge of the District of Montana since 2008.
Cebull's notable cases include his block of reopening of the U.S. border to cattle in 2005, two years after the U.S. banned Canadian cattle and beef products over fears of mad-cow disease. The 9th Circuit overturned that decision.
Cebull also presided over a lawsuit filed by landowners against Exxon Mobil Corp. over the cleanup following last year's pipeline spill of 1,500 gallons into the Yellowstone River.