The MSPs said Scotland should adopt a “housing first” scheme, similar to a strategy used successfully in Finland.
The Local Government and Communities Committee said the plan, which has been piloted in parts of Scotland, should go nationwide.
The housing minister has welcomed the committee’s report and said he will consider it carefully.
The model being proposed prioritises a homeless person’s unconditional right to a permanent home, without them having to go through several levels of temporary accommodation first.
In Finland, the committee said, it has helped it become the only country in Europe where homelessness has declined.
“In many cases, it was found that for those who had problems with substance and alcohol misuse, their using reduced dramatically or stopped when they were given a secure tenancy and the right support,” the committee’s report states.
Convener Bob Dorris said: “After hearing directly from people who are homeless and those who have experienced sleeping on the streets or sofa-surfing, as well as service providers on the front-line, it was clear that further action is needed.
“That’s why our committee has recommended that the Scottish government learns from Finland and rolls out a Scottish version of Housing First, as a part of a potential solution to addressing homelessness.”
The latest figures show councils received more than 34,800 applications for homelessness assistance in the year to September 2017.
Housing Minister Kevin Stewart said: “Scotland has some of the strongest housing rights for homeless people, but as this report highlights, for some people – who may have more complex needs or be rough sleeping – simply providing accommodation is not always enough.”
Mr Stewart added: “The committee has highlighted a number of important areas for further work which I will consider fully and carefully.”