Mr O Muiri described the availability of WifFi at 12 locations as "one of the milestones that will deliver on our Digital Dublin Initiative".
The WiFi hotspots will be identified by wall mosaics featuring 'digidub' characters, ancient and modern.
Fourteen different characters will be rolled out, including a Viking, a street cleaner, a tourist, a rockabilly girl and pyjama girl.
"These signs are a fun and attractive way to advertise the city's WiFi hotspots.
"Dubliners will be invited to suggest additional characters," the council said.
Mr O Muiri said: "Our future economic success, our ability to attract talent and investment and our competitive branding internationally means we have to use and apply digital technologies now."
He added that by June the city will have a digital masterplan.
"The aim of the plan is to develop Dublin as a world centre of digital excellence," the Lord Mayor said.
He also asked Dubliners to identify and suggest different uses that can be made of the availability of free WiFi in terms of developing services, encouraging people connecting, and making the city more attractive.
To mark the launch, the public is invited to take part in a Twitter Wifi Day from 11am to 5pm at Barnardo's Square.
Anyone sending one tweet (using #DublinGowexFreeWifi) will be entitled to one day of free premium WiFi (speed up to 6Mbps).
Those registering as a user of the WiFi network on launch day will be in with a chance of winning a Nexus 7 Tablet.
The free WiFi locations are: Smithfield Square; Barnardo's Square; Clarendon Street; St Patrick's Park; O' Connell Street Plaza/GPO; Temple Bar Square; Wolfe Tone Square; frontage to the Convention Centre Dublin; Merrion Park; Henry Street; Grafton Street; outdoor amphitheatre located at Civic Offices.