Former Rep. Trey Radel (R-Fla.). (AP)

A House ethics investigation into now-former Rep. Trey Radel (R-Fla.) has formally concluded its work because he is no longer in office.

The House Ethics Committee announced the formal end of its probe Wednesday, saying in a statement that it no longer has jurisdiction over Radel.

Radel resigned Monday only a few weeks after returning to his job after a stint at a rehabilitation center in Florida. Radel was arrested in November and charged with misdemeanor cocaine possession. He pleaded guilty and agreed to seek treatment at the rehab center. But he initially refused to resign, saying he would first try to get healthy and then seek to reclaim the trust of his constituents and colleagues.

The ethics panel launched a formal probe into Radel's actions on Dec. 12, but said Wednesday that it "unable to complete its work" before Radel resigned.