Nicholas and Mackenzie Spencer accepted the charges under a deal which saw far more serious charges dropped.
They had been charged with child trafficking and torture, for which they could have faced life in prison.
The pair made the boy sleep on a wooden platform and fed him cold food.
Their nanny reported the “repeated unbecoming inhumane treatment” of the boy, who has special needs, to local police last December.
The boy had lived with the couple, originally from South Carolina, for two years before they were arrested last year.
They also pleaded guilty to degrading treatment, working illegally and unlawfully staying in Uganda without permits.
For this charge they were sentenced to two months in prison, which they have served after they were arrested last year.
High Court judge Alice Kyomuhangi also ordered them to pay the victim compensation of 100 million Ugandan shillings ($26,000: £22,000).
“The child was in need of help and support, having lost his father and having been abandoned by his own mother. Unfortunately the accused persons failed to manage his peculiar behaviours,” the judge said while delivering her ruling.
David Mpanga, the couple’s lawyer, told the Reuters news agency the boy had psychiatric issues and that the pair failed to look after him properly because they had no parenting experience.
The couple fostered three children in Uganda, where they moved in 2017 to work as volunteers.
This case has sparked outrage among some Uganda child rights activists, who called it a mockery of justice.
Activist Proscovia Najjumba asked how the couple were allowed to “walk away” after accepting they “mistreated a child”, reports AFP.
Darren Namatovou, founder of Children Phoenix Foundation, told the BBC that due diligence and background checks needed to be done thoroughly during the adoption process in order to prevent cases of child abuse.
International adoptions are controversial in Uganda.
The law was tightened earlier this year, to remove what the government said was a loophole used for child-trafficking.