He has interim name suppression and will sentenced next month.
Crown prosecutor Clayton Walker opposed the elderly man's name suppression.
Uetaha's mother, Ailza Wanoa, and several other family members and supporters were sitting in the public gallery when the man entered his plea.
The tragedy occurred at Kirkpatrick Park in Hastings on October 8, 2013, where witnesses said Uetaha was killed when he was run over by the tractor-mower. Police said at the time of the incident the toddler was believed to have been at the Camberley park with older cousins.
Uetaha's family affectionately called him "Bubbies" and described the little boy as a "bubbly, cheeky" toddler.
The 4-year-old was looking forward to starting at Kura Kaupapa o Heretaunga School in Hastings.
The 72-year-old driver, who worked for the Hastings District Council, will appear for sentencing in July.
He has been with the council for 13 years and was a senior driver, but has not mowed council land since the incident.
However, he has continued to be employed by council, performing other duties, and will retire on June 6.
Hastings Mayor Lawrence Yule said neither he nor the council was in a position to comment on the case before the driver was sentenced.
Hastings District Council is also being prosecuted over the death by the Government's workplace safety agency, WorkSafe New Zealand.
The charge relates to Section 15 of the Health and Safety in Employment Act 1992, under which employers need to take all practicable steps to ensure that no action or inaction of any employee while at work harms any other person, and carries a maximum penalty of a $250,000 fine.
