The city is being divided into four areas, each being serviced on a separate day with no collections on a Monday.
The changes will save up to Â£500,000 a year with the bin lorry fleet reduced by five to 21, the council said.
No staff will be lost as fewer agency staff will be hired. Households have been sent information packs about the changes to the collections.
Residents have been asked to check their packs to find out their new bin day and which bin is due to be emptied.
Councillor Chris Poulter said: "Anyone not yet sure of the day or which bins to put out, should check their information pack, which gives full details, or they can check on the website by simply inputting their post code."
Four out of five households will see their collection day change.
The city crews collect about 114,000 bins every week.

The crash, which involved the bike and a Range Rover, took place at about 19:30 BST on Saturday at Groesonen Road in Clytha, near Abergavenny.
The driver of the Range Rover was arrested on suspicion of causing death by dangerous driving.
The motorcyclist, from Bristol, was pronounced dead at the scene.

NICE, the advisory body for the health service, has already been exploring the issue.
But it now wants to know what the public thinks after the idea got the thumbs up from its citizen's council.
Nearly two thirds of the 32-strong group - used as a sounding board for sensitive topics - backed incentives.
In May, NICE officials told the BBC incentives could play a key role in tackling smoking, obesity and drinking rates and was working with academics to see how and when they worked best.
Merit
Its citizen's council agrees the idea has merit - as long as the payments are not allowed to be used for unhealthy pursuits.
The backing has prompted the public consultation which will be run until the end of November.
Incentive schemes are already operated in some areas to mixed success, while NICE has already backed their use for drug users.
However, it is unlikely the current government would allow NICE to formally recommend incentives as an option for the whole health service.
A Department of Health spokesman described them as an undesirable use of money and should only be adopted as a "last resort".
Instead, it seems the only way the advisory body would end up backing them would be for niche groups, such as specific age groups or for people from certain social backgrounds, if there was strong evidence they worked.
NICE chairman Sir Michael Rawlins said: "We clearly face several public health challenges in today's society, some more obvious than others, and we must seek to improve these in ways that are likely to achieve the best health outcomes for those affected."
Derby City Council are changing bin collection days and times from 6 June.
[NEXT_CONCEPT]
A motorcyclist has died after a crash in Monmouthshire, Gwent Police has said.
[NEXT_CONCEPT]
A public consultation is being launched over whether the NHS in England and Wales should offer financial incentives to encourage healthier lifestyles.