There will also be new fortnightly collections for soft plastics and cartons.
New communal wheelie bins will be issued with different coloured lids to help residents to separate their waste properly.
Councillor Richard Wilkins, who is in charge of waste services at Somerset Council, said: “People in flats have been asking to be able to do more recycling for an awful long time, this will enable them to do this.
“Change is always difficult, but from my understanding, we’ve made this as easy as possible.”
The changes are funded by the government’s Simpler Recycling programme.
Recycling of soft plastics will not be made mandatory until 2027.