NEW YORK (Reuters) - The New York District Attorney's Office will not bring sexual assault charges against Greg Kelly, ending a two-week probe of the local television host who is also the son of New York City Police Commissioner Raymond Kelly, the prosecutor's office said Tuesday.

"We have determined that the facts established during our investigation do not fit the definitions of sexual assault crimes under New York criminal law," a letter from the head of the DA's sex crimes unit, Martha Bashford, to Greg Kelly's attorney, Andrew Lankler, said. "Therefore, no criminal charges are appropriate."

The investigation began on January 24 when a sexual assault complaint was filed against Kelly with the New York Police Department, stemming from an October 2011 incident, the letter said. Reuters obtained a copy of the letter.

The police turned the investigation over to the DA's office to avoid any conflict of interest that could arise from city police conducting a criminal probe of the son of the department's commissioner.

"We conducted a thorough investigation, consistent with what the sex crimes unit does with regularity in similar matters," Bashford said in the letter.

The prosecutor said her office interviewed both Greg Kelly and the complainant, a woman who has not been identified by investigators. Both were cooperative witnesses, Bashford said.

NYPD spokesman Paul Browne said Ray Kelly would have no statement on the matter.

Greg Kelly has been on a leave of absence from his position as co-host of "Good Day New York" on Fox television station WNYW since news of the probe broke two weeks ago.

Neither Greg Kelly nor his attorney could be reached immediately for comment. In previous statements, Kelly's attorney, Lankler, has said his client denied any wrongdoing.

(Reporting By Joey Ax and Jonathan Allen; Writing by Dan Burns; Editing by Cynthia Johnston)