The project will cost up to £11m, said Edinburgh City Council chief executive Sue Bruce. Becoming a "super-connected city" would enable it to compete with the world's top digital cities and attract new jobs and investment, she added.
"Free public Wi-Fi zones will be focused initially in the city centre, with the potential to extend to key cultural and community locations across Edinburgh," she said.
Westminster is funding the work in the £100m Super-Connected Cities Initiative. Edinburgh will publish a detailed plan by July, outlining how the money will be spent.