Police Scotland launched an investigation after a complaint was made against Mr Logue that he was the director of two unauthorised council subsidiary companies; ESCA UK Ltd and No Limits Leisure Ltd (NLL).
However, the probe has now ended after Police could find no evidence of wrongdoing.
In a statement, Cllr Logue said: "It is no surprise that Police Scotland has found no substance to the spurious allegations made against me.
"This whole episode has been a waste of time for the police and for the council. In my view, the police should consider the extent to which their valuable time and resources have been wasted by the people behind this farce.
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"I have been a councillor for 40 years. 30 years ago I put my political prospects on the line to expose wrongdoing by members of my own party in Monklands District Council. Last year, I ensured there was a proper investigation into allegations of corruption in procurement based on anonymous but credible allegations, something other politicians would be extremely cautious about doing.
"Anyone who knows me and the way I go about my business knows that I would never be involved in fraud or corruption of any kind. I am very grateful for the support of my family and my colleagues during what has been an extremely difficult time.
"This whole episode has been a failed smear attempt. But the people who are complicit in that smear attempt should know this: I will never be diverted from my role in leading a forward-thinking council which achieves, and will continue to achieve, great things for the communities of North Lanarkshire.
"My focus is now on delivering the biggest council housebuilding programme in a generation in Scotland, on delivering record levels of economic growth, on building half a billion pounds worth of new schools. These are the things that matter to the people of North Lanarkshire."
(LM/MH)
