The Scottish Environment Protection Agency (Sepa) began exploratory work in May to find traces of the virus's genetic footprint, similar to DNA.
Analysis of the collected samples has identified RNA in waste water from 12 of Scotland's 14 health boards, with only Shetland and the Western Isles in the clear.
The results have been shared with Public Health Scotland (PHS) and are consistent with areas known to have confirmed Covid-19 cases.
Terry A'Hearn, Sepa chief executive, said: "As Scotland's environmental watchdog and as a public agency, we remain proud to be playing our part in the national effort to combat coronavirus.
"Our scientific capabilities and expertise in designing and implementing monitoring networks made us ideally suited to delivering this trial and the results we are seeing demonstrate its scientific validity.
"Central to the delivery of this project has been our partnership working with Scottish Water and the University of Edinburgh's Roslin Institute, and we will continue to work closely together to refine our techniques and understanding.
"We've received support from across the public sector, agencies and institutions - including a donation of specialist kit from Science and Advice for Scottish Agriculture - demonstrating how Scotland is coming together to find ways of tackling this virus."
Samples are collected by Scottish Water and its operators at 28 public waste water treatment works across the country.
The World Health Organisation has said there is currently no evidence Covid-19 has been transmitted via sewerage systems.
But in the Sepa research, analysis of Aberdeen found prevalence of the virus mirroring cases in the population at the beginning of August.
The sampling rate was increased to four times a week to provide more information and there was then a gradual decline to below the level that concentrations can be detected with sufficient accuracy.
Results remained at the same level until the end of September before they began to rise again, reflecting PHS data on known cases.
The Sepa team is also assisting UK government scientific advisers who are investigating how waste water monitoring can be used to track the transmission of coronavirus.
The Scottish Government's Environment Secretary Roseanna Cunningham said: "In order to manage the coronavirus pandemic, it is vital that we continue to develop our understanding of it.
"I welcome this UK-wide programme of research and the development of waste water monitoring to help build our knowledge base.
"Sepa and Scottish Water have translated this experimental programme into a comprehensive, Scotland-wide monitoring network.
"The early data is already providing our public health experts with new information, which complements the wider population testing programme to give a more robust picture of the prevalence of Covid disease in Scotland.
"I look forward to the programme providing further, valuable data over the coming months to support our fight against the pandemic."
The Sepa data has been made available online at https://informatics.sepa.org.uk/RNAmonitoring/.