It comes after Mr McArthur lodged a final proposal in early September, initiating a 30-day window for him to garner cross-party support from at least 18 MSPs.
This goal was reached within two hours.
Mr McArthur aims to introduce a Bill in early 2023 that would allow mentally competent adults who are terminally ill to end their lives.
Two doctors would need to confirm a person was terminally ill and mentally competent, and there is a suggested reflection period of 14 days.
More than 14,000 individuals and organisations responded to a consultation on the plans – the largest ever public response to a members' bill in Holyrood.
A clear majority, 76 per cent, backed the legislation.
However, critics have raised numerous concerns. Labour MSP Pam Duncan-Glancy, a wheelchair user, previously called the plans "dangerous for disabled people".
Mr McArthur said: “I would like to offer my sincere thanks to all MSPs who have put their names behind my proposed change in the law.
"The support among colleagues has been deeply heartening, and demonstrates the growing recognition that there is a need to end the ban on assisted dying in Scotland.
“The Scottish public has long been ahead of the parliament on this issue.
"The public consultation on these proposals, published last month, demonstrated that there is strong and passionate support for offering people more choice at the end of their life.
“I now look forward to working with colleagues in parliament to bring forward a safe, robust, and compassionate Bill.
"I remain committed to a process which carefully considers the views of the public, organisations and healthcare professionals, as well as international experience, to craft legislation which is tightly drawn and contains strong safeguards.”
Dr Miro Griffiths, an expert on disability policy and spokesman for the Better Way campaign, which opposes the Bill, called on MSPs to reject it.
He said: “In nations where assisted suicide and euthanasia are legal, we have seen an undeniable lapse in the value ascribed to human beings.
"Disabled people and people with mental health conditions are not given the respect, protection, and affirmation they deserve.”