A disciplinary hearing was told he sent the videos to the woman, 35, after working his shifts.
He admitted sending the messages but denied filming them while he was on duty.
After he was caught, he told senior officers that when he was unable to see the woman, they would send explicit messages and videos to each other.
The hearing was told the woman was "vulnerable to an abuse of trust or power".
The constable, who had worked in the force for five years, denied misconduct but was dismissed without notice by a disciplinary panel.
Jonathan Walters, representing South Wales Police, told the hearing that Leach met the woman while following up a crime report.
She was a potential witness in a case he was investigating.
Leach told the hearing he wanted to forge a friendship because the two "had a lot in common" and were both "professional people".
"It was Leach's intention to begin a sexual relationship," Mr Walters said
He said that Leach – who was in a relationship with another police officer – set out to "weave his web" and "blur the lines between a professional and personal relationship".
Leach was found to have made five breaches of standards of professional behaviour amounting to gross misconduct.
He also had two breaches of "honesty and integrity" after misleading his supervisor by failing to disclose the full extent of contact between himself and the woman.
