Lord Hardie said he wanted to hear from anyone affected by the failure to complete the project on time and on budget.
His team is already sifting through five million official documents.
Lord Hardie said: "The Edinburgh Tram Inquiry must base its findings on direct evidence from those affected by the planning and construction phase."
He added: "Whether a local resident, business, developer or other interested party, this is the public's opportunity to offer views on the direction of the inquiry and to provide evidence for consideration."
Trams started running last year on the 8.7-mile (14km) route between Edinburgh's New Town and Edinburgh Airport, which cost Â£776m to build.
An inquiry into the project was commissioned by Scottish ministers in June 2014. Its terms of reference are to:
In November last year, the Scottish government announced Lord Hardie's investigation was to become a statutory inquiry.
This gave him the power to compel individuals and organisations to co-operate.
In a BBC interview, Lord Hardie said the move was necessary because some people had refused to co-operate, or had failed to respond to his requests.
The deadline for submitting written evidence to the inquiry is 4 August.
The man in charge of the Edinburgh tram inquiry has called for help from the public.