Dundee West MP Chris Law was detained last September in a probe connected to his Spirit of Independence referendum campaign in 2014.
The campaign saw him raise grassroots funding to travel across Scotland in a Green Goddess fire engine, drumming up support for the Yes side.
The Crown Office confirmed that no further action would be taken.
A spokesman said: “Following discussion with Police Scotland, we agree with their assessment that there is insufficient evidence to support each of the allegations, and that as such they do not intend submitting a formal prosecution report.”
Mr Law told the Courier newspaper: “Politics - at all levels - should be a force for good. That’s what drove me to become involved in the referendum campaign with Spirit of Independence, and why I stood to represent the people of Dundee West.
“While this has been a distressing process, I have always continued doing the job I was elected to do and I am now more motivated than ever to stand up for my constituents.
“While there was never any doubt from the outset, I was happy to co-operate with inquiries and I’m glad the matter has now been fully resolved.”