The council has signed an agreement to work with Openreach to improve digital connectivity in the city, increasing coverage, choice and speed.
Councillors welcomed the news but council leader Julie Dore said many people were still unsure about using the internet.
She told a meeting: “There are some negatives potentially and we need to be aware, identify them and take them into account.
“There is still some stress associated with going online and I know from personal experience with my parents.
“We have a certain generation that are used to having the same gas supplier all their life and doing things through the Post Office and bank and they have a fear of doing things online.”
Council tenants will be given help to get online but Coun Jackie Drayton, cabinet member for children and families, said many poorer people lived in privately rented homes.
She said: “We have five wards where child poverty is over 50 per cent and most live in rented rather than social housing in the poorest areas.
“Have we thought of looking at what works to help people through austerity as people in poverty are furthest away from this. We want these isolated people to take part in this world and have social interaction.”
Coverage of superfast broadband in Sheffield is at 96.5 per cent of the city and coverage of 4G ranges from 72.1 to 96.2 per cent of the city depending on network operator.
However, both superfast broadband and 4G technologies can’t meet future demands for speed, capacity, reliability and responsiveness, and are fast approaching the end of their lives.
The next generation of digital connectivity consists of full fibre networks and 5G.