From 1 January, people must show a driving licence, council tax bill or a utility bill to use sites in Lamby Way, Wedal Road and Bessemer Close.
The council said 17% of users at Bessemer Close were from a neighbouring authority.
It said such "cross border movement" costs the council Â£430,000 a year.
Bob Derbyshire, cabinet member for environment, added: "It therefore seems fair to me that if residents from outside our catchment area want to use our facilities they should be asked to either pay for using it or directed to their own authority's HWRC [Household Waste Recycling Centre]."
New seasonal reduced opening hours will also start in 2016 to account for reduced demand during the winter months.
From 2 January, the site will open from 09:30 GMT with last entry at 18:00, while weekend openings from 10:00. Longer opening times will return in the summer.

Deborah Leonard did not feel she could stand up to other members of the Word of Life church in New York state, said her lawyer, Devin Garramone.
Her son Lucas, 19, died from the attack and his brother is in hospital.
Police say they were beaten by Mrs Leonard, her husband and five others in order for them to confess their sins.
All six people arrested, including the boy's father and sister, have denied the charges.
"It looks like she went along with it, and it spun out of control," said Mr Garramone, who described the incident as an "intervention".
"This woman is so meek and timid, she didn't have the temerity to stand up to them and say, 'You're not punishing my kid. You're not doing this.'"
Some of the others arrested may have caused the fatal injuries, he said.
The boys were repeatedly kicked and punched on Sunday but it's not clear why.
Police have described the beating as a "spiritual counselling session to urge [the boys] to confess sins and seek forgiveness".
Ms Leonard's husband Bruce, who founded the secretive church in New Hartford, New York, said it was a family meeting that had nothing to do with the church.
Lucas died on Monday morning in hospital, where his parents took him the morning after the attack.
His 17-year-old brother Christopher remains there in a serious condition.
The parents have pleaded not guilty to manslaughter and the other four have pleaded not guilty to assault.
The Word of Life church is nearly 30 years old and its membership has fallen in recent years from about 40 to 20, said a local police chief. Some live at the church.
The church refused help from firefighters when the building caught fire a few years ago, he said.
Residents in Cardiff will have to prove where they live before they are allowed to use the council's waste recycling centres.
[NEXT_CONCEPT]
A woman charged with beating her son to death in a church has said she "felt helpless" to prevent the violence committed by other church members.