Mr Matheson, who denied the allegations, was facing a four-week suspension and had been asked to stand down as City of Chester MP by Labour.
The Independent Expert Panel had released a report recommending the suspension, after the Parliamentary Commissioner for Standards Kathryn Stone upheld two allegations of sexual misconduct against Mr Matheson by a former member of his staff, made under Parliament’s Independent Complaints and Grievance Scheme (ICGS).
“I have today, with great sadness, tendered my resignation as Member of Parliament for the City of Chester,” Mr Matheson said in a statement.
“I am dismayed that I have been found guilty of several allegations that I know to be untrue.”
Ms Stone concluded that Mr Matheson had invited his former member of staff on a private trip abroad and “the invitation was sexually motivated, unwanted, and had placed the complainant under pressure and intimidated her”, according to the report.
During a work event outside Parliament, he had also “linked arms with her; made personal comments about her appearance while looking at her suggestively; made her hold his hand as they left and insisted on accompanying her to her bus stop; and once there invited her back to his flat, kissed her twice on the forehead and attempted to kiss her on the mouth. The Commissioner concluded that these were all unwanted and unwelcome sexual advances”.
It is understood that the Labour Party launched an investigation and immediately suspended Mr Matheson from Labour Party membership in light of the report. The Chief Whip told him he had lost the whip and urged him to stand down as an MP.
A Labour spokesperson said: “This is an incredibly serious case. There must be a zero tolerance for sexual harassment and the Labour party has acted immediately following the ICGS findings.
“We will now select a candidate that the people of Chester can be proud to vote for.”
Mr Matheson’s resignation will trigger a by-election in the City of Chester.
In his resignation statement, Mr Matheson said: “From the start I accepted I had committed a minor breach of the code and had hoped that an honest and open approach would stand me in a fair light.
“This has proven not to be the case and I am dismayed that I have been found guilty of several allegations that I know to be untrue. Indeed my insistence on what I know to be true – that I had no sexual motivation in this matter – was held against me as a refusal to accept my guilt, and caused an increased sanction which I felt was disproportionate.
“Despite provable factual inaccuracies in the sanctions report, my appeal against sanction was not even considered, for the same reason.
“Therefore, I faced a suspension from the House of four weeks. Whilst I believe that this is an excessive and unfair penalty, I cannot challenge the process further.
“I believe that the honourable and right thing to do now is to resign my seat and seek to rebuild my life elsewhere.”