Smith died by lethal injection of pentobarbital at 10:29 a.m. for killing Autumn, the daughter of his live-in girlfriend, Kesha Frye, the Mansfield News Journal reported.
Autumn's aunt, Kaylee Bashline, lifted her arms in celebration at the news of his execution.
Frye and her father, Patrick Hicks, also attended as representatives of the victim.
Smith's daughter, Brittany Smith, and niece, Melissa Aguirre, were there to represent him, as was public defender Joseph Wilhelm.
"This horribly disgusting crime that he committed has affected our family in many ways," Hicks said in a prepared statement after the execution. "Not only was an innocent child's life taken by his hand, but the images of his actions have been engraved into all of our hearts and minds.
"He has shattered the lives of our family and his own. ... Because of him, Autumn never had a chance to take her first step; she never had her first birthday or a first day of school. There is no excuse that could ever justify what he did and the heartache he has caused. It's just unfortunate that he gets to die peacefully after the torture he put Autumn through."
Smith declined to make final remarks before being put to death, and his representatives declined to address reporters afterwards.