Manhattan prosecutors will not seek rape charges against Greg Kelly, the TV talk-show host and son of Police Commissioner Ray Kelly, stemming from a complaint filed by a 29-year-old Manhattan woman, authorities said tonight.

The sensational case was nearly over as soon as it started — after it surfaced that his accuser engaged in steamy texts with him after their sexual encounter, suggesting they get together again, sources said.

“Those aren’t the words of a woman raped,’’ one law-enforcement source flatly told The Post.

Another source said the later texts showed that “the lustfulness for each other was mutual’’ and added that it should be “no surprise’’ that the investigation was dropped.

“Between her story, her texts, his story, the small amount of alcohol [involved that night], there was just no evidence,’’ the source said. “The only theory was that she was physically helpless, not forced, but there was no proof that she was in a drunken stupor.’’

The source said the accuser would not be charged with anything because the alleged attack appears to still be her perception of what happened the night of Oct. 8 in the law office where she works as a clerk.

“There are no plans to prosecute her because [prosecutors] don’t believe she is lying. She never wavered from her story that she was too drunk to consent,’’ the source explained. The accuser, who has a boyfriend, had met Kelly two days earlier at the South Street Seaport. She claimed that he got her so drunk that she couldn’t consent to sex.

She waited three months to report the incident.

Kelly, 43, an unmarried ex-Marine and popular host of Fox’s “Good Day New York,’’ responded in a statement through his lawyer:

“I am thankful that the investigation established what I’ve known all along, that I am innocent of the allegations that were waged against me.

“I am so blessed to have a wonderful family and friends whose support for me never wavered.”

He gave a special shout-out to his loyal co-host, Rosanna Scotto.

“I will always remember her kindness, and I look forward to soon resuming my post on “Good Day New York” next to her,” he said.

Kelly’s dad, the city’s top cop, declined to comment.

The Manhattan DA’s office said it had informed both Kelly and the accuser earlier in the day that no charges would be brought.

“After reviewing all the evidence, we have concluded that the established facts do not constitute a crime under New York criminal law,’’ said DA spokeswoman Joan Vollero in a statement.

“From the moment this matter was referred to this office, we conducted a thorough investigation, consistent with standard practice. That investigation included interviewing numerous fact and expert witnesses, and reviewing and analyzing multiple items of physical evidence, including, but not limited to, receipts, security logs, text messages and telephone records. “ In the letter sent to Kelly’s lawyer, Andrew Lankler, the DA called both the accused and accuser “cooperative’’ in their interviews, but concluded that “no criminal charges are appropriate.’’

At one point, the accuser claimed that she had gotten pregnant by Kelly and had an abortion.

But a law-enforcement source said at the time, “It sounds like a bunch of BS.”

Another source said, “It sounds like she got caught [cheating] by her boyfriend, and then he forces her hand: ‘If you’re not lying, you better ­report.’ ”

Additional reporting by Larry Celona