The group is the latest to resort to fines after several local authorities introduced penalty notices. Royal Parks chief inspector Simon Davis said a minority of the 40 million visitors to the parks each year "flagrantly" broke the rules.
Kirklees Council in West Yorkshire also introduced fines last week for dog owners who do not clean up after their pets or fail to keep them under control in public areas including its five major parks. Dogs are banned from children's play areas.
Failure to pay the £75 charge could lead to a court fine of £1,000. The new penalty notices followed a public consultation after the council received more than 4,200 complaints on dog fouling and 2,000 about dangerous dogs in two years.
Meanwhile, the number of fines issued for dog fouling in Blaenau Gwent has soared from 10 to 1,099 in a year after the local authority hired a private firm, according to the BBC, which used a freedom of information request.
Fife Council has dished out fines of nearly £4,000 in two years to dog walkers for not bagging up after their pets.
Some 112 offenders were caught and fined up to £40 each for breaking the Dog Fouling (Scotland) Act. Doncaster Council has also introduced £50 fines and a how-to guide on poop-scooping.