Speaking outside the court Greater Manchester Police made this statement on behalf of Rio's family:
The family said; "we wish we could say that we can start to rebuild our lives, but the hard work is just beginning."
Police have released CCTV of Daniel Rigby with two-year old Rio Smedley the day before he killed the toddler.
Jan Urey, of the Crown Prosecution Service, said:
Mr Justice MacKay adjourned Smedley's sentencing to a date yet to be fixed for the preparation of a pre-sentence report, and remanded her into custody.
He told her: "I want you to understand that you stand in very real peril of a prison sentence as a result of this conviction. Don't have any delusions about it."
Detective Chief Inspector Phil Reade of Greater Manchester Police said: "This is a shocking case in which an innocent and defenceless little boy has suffered appalling injuries at the hands of someone who had been trusted to look after him.
"Rigby has today been put behind bars for a long time for his actions, but this will go little way to ease the suffering of Rio's family, who have lost their beloved little boy under such tragic circumstances."
The jury took four and a half hours to reach the two unanimous guilty verdicts.
As the guilty verdict was read out on the murder charge, there were gasps from the public gallery and some of Rigby's relatives left the court in tears.
Rigby, dressed in a grey suit, shirt and tie, put his head in his hands as the verdict was given.
Smedley, dressed all in black and with her dark hair tied back, appeared to be struggling to hold back tears when the jury announced her guilty verdict.
Sentencing Rigby, Mr Justice David MacKay told him:
The judge said he did not think Rigby intended to kill Rio but had a "sudden loss of temper" and "set about him, inflicting the fatal blow".
Daniel Rigby was given a life sentence and ordered to serve a minimum term of 17 years before he would be considered for parole.
Earlier the court was told that Rio's injuries were likely to have been caused by "heavy blows" from "punches, kicks, knees and stamping".
Simon Phillips QC, for the prosecution, accused Rigby of "striking Rio with such force as to split his liver in two" at around 4.30pm on April 22 this year.
He said the attack was part of "a sustained and violent attack".
He added: "A wicked attack on a defenceless two-year-old child."