Public spaces protection orders (PSPOs) were drawn up following a four-week public consultation in February and March.
The new orders give police and council officers greater powers to tackle behaviour that has a "detrimental effect on the quality of life of the local community".
They will be able to issue £100 on-the-spot fines to anyone caught drinking alcohol, using psychoactive substances, urinating, defecating, loitering or begging in public.
Councillors approved the orders after they were told that, of the 225 people who responded to the consultation, between 90% and 98% supported the inclusion of each behaviour.
The PSPOs, which came into force on Friday (June 23), will remain in place for three years but that can be extended if similar anti-social problems remain.
Full details, including maps of the areas covered by the PSPOs, are available at www.rushmoor.gov.uk/pspo.
Councillor Ken Muschamp, RBC’s cabinet member for safety and regulation, said: “The PSPOs will strengthen our ability to deal with the issues we are experiencing in our town centres.
“They will give both the council and the police the chance to respond more flexibly to the worst kinds of anti-social behaviour.
“The consultation showed that those who live, work and own businesses in the town centre are keen for us to take a more pro-active response to these issues.”