By Richard Cowan and James B. Kelleher

WASHINGTON/CHICAGO (Reuters) - Representative Jesse Jackson Jr., who has been treated for bipolar disorder and is reportedly under investigation for alleged misuse of campaign funds, resigned his seat on Wednesday.

The Chicago Democrat said in a letter to U.S. House Speaker John Boehner, said: "My health issues and treatment regimen have become incompatible with service in the House of Representatives. Therefore, it is with great regret that I hereby resign ... effective today, in order to focus on restoring my health."

Jackson, the 47-year-old son of civil rights leader and presidential candidate Reverend Jesse Jackson, also admitted to "my share of mistakes," in his two-page letter to Boehner, an Ohio Republican.

"I am aware of the ongoing federal investigation into my activities and I am doing my best to address the situation responsibly, cooperate with the investigators, and accept responsibility for my mistakes, for they are my mistakes and mine alone," Jackson wrote.

Jackson has been in Congress since 1995 and easily won re-election in a heavily Democratic district earlier this month despite his ailment and the ethics questions hanging over him.

His resignation is not expected to result in any changes in the political balance of power of Congress, which is controlled by Republicans.

Jackson was treated for at least six weeks at the Mayo Clinic in Rochester, Minnesota, this summer for bipolar disorder, a psychological condition marked by extreme mood swings, and has been on medical leave from the House since June.

In addition to his health issues, Jackson has been the subject of a House ethics committee probe over an alleged bribe offered by a Jackson supporter in 2008 to then Illinois Governor Rod Blagojevich.

The bribe was said to be intended to entice Blagojevich to appoint Jackson to the U.S. Senate seat vacated by President Barack Obama. Jackson has admitted to lobbying for the seat, but denied knowing about any money offered to Blagojevich, who has since been convicted on corruption charges and imprisoned.

According to news reports citing unnamed sources, Jackson is also being investigated by the FBI over possible misuse of campaign money. The FBI has not confirmed the reports.

In his letter to Boehner on Wednesday, Jackson acknowledged a probe was underway and said he hoped it would not overshadow his years of public service.

"None of us is immune from our share of shortcomings or human frailties and I pray I will be remembered for what I did right," Jackson wrote.

Emails and calls to Rep. Jackson's Washington D.C. and Chicago offices, as well as the office of Jackson's father, civil rights leader the Rev. Jesse Jackson, seeking comment on the resignation were not immediately returned.

(Additional reporting by David Bailey; Editing by Jackie Frank)