Mr McDonald accepted his behaviour had caused “hurt and offence” to two women and offered them a “public and unreserved apology”.
While the former minister said he was resigning from the SNP with immediate effect, he confirmed he is to stay on as an MSP for the Aberdeen Donside constituency.
The politician, who has been absent from the Scottish Parliament since the allegations against him were first made in November 2017, now plans to return to Holyrood next week and will sit as an independent MSP.
SNP bosses launched an investigation into “reports of inappropriate behaviour” by the married father-of-two, with allegations made by three women.
The findings were shown to Mr McDonald on Monday.
The report has not been made public – with the SNP facing calls from the Conservatives to do so “so that the public can judge whether he is fit to remain as an MSP”.
It is understood investigators concluded the MSP’s “inappropriate behaviour had been deliberate in nature” and he should have known not to act in this manner.
His behaviour is said to include sending inappropriate and unwanted text and social media messages, causing distress to women through his unwanted attention and exploiting his position of power, with the investigation finding there had been “persistent behaviour over an extended period of time”.
Mr McDonald said: “I have accepted that my behaviour towards two individuals fell below the level of professionalism that they were entitled to expect of me, whether in a professional or a social context.
“While at no stage was my behaviour in any way physically abusive, and while it was certainly not my intention to cause any upset, discomfort or offence to those concerned, it is clear through the concerns highlighted in the report that I have done so.
“That is something which I deeply regret. I would like to take the opportunity here and now to offer a public and unreserved apology to those individuals for the hurt and offence that I have caused them.”
Mr McDonald stood down from his post as childcare and early years minister with the Scottish Government on November 4 2017 after allegations were first made.
He was suspended by the SNP 12 days later after fresh claims were made against him.
The MSP said he was first informed of the allegations he was facing on January 14 2018, adding that it was four days later when he was interviewed that “the precise detail behind those allegations was placed before me for the very first time”.
He went on to state that on February 9 he had been told the report would be ready in “days rather than weeks” – but added it was March 5 before he was allowed to see its findings.
An SNP spokesman said: “The findings of the independent investigation were shared with Mark McDonald on Monday and the SNP group was due to consider disciplinary action, based on those findings.
“Investigators concluded that Mr McDonald had been deliberate in his actions and should have been aware that it was not appropriate for an individual in his position to be behaving in such a manner.”
Tory MSP Alexander Burnett said the SNP must “come clean” and publish the report into Mr McDonald’s behaviour.
The Conservative said: “Many people will rightly be questioning why Mark McDonald thinks that his behaviour was bad enough to resign from the SNP, but not to resign from the Scottish Parliament
“He is clearly prioritising the reputation of the SNP over that of Holyrood and it’s simply not good enough.
“This saga has dragged on for months yet we still don’t have any detail on the allegations against Mark McDonald.”
Labour parliamentary business manager Rhoda Grant said: “Mark McDonald decided his conduct was not fit for a minister or an SNP MSP – but somehow it is acceptable for an MSP without party affiliation.
“People in Aberdeen Donside will rightly question that. It looks like Mark McDonald has put the reputation of the SNP before what is best for his constituents.”