The boyfriend will be sentenced for rape and for causing or allowing Baby P's death in August 2007. Baby P's mother and lodger Jason Owen, who was convicted of the same charge over Baby P, will also be sentenced.
The judge will be able to pass a life sentence on the boyfriend if he considers him to be a danger to the public.
Judge Kramer told the couple: "The likelihood is of very substantial sentences in both cases."
Baby P died in Haringey after suffering months of abuse and despite visits by the authorities.
In the latest trial, the girl - now four years old - became the youngest child to give evidence at the Old Bailey, through a video link.
The court was also shown her video interview with police when she was three, in which she said the man had hurt her.
Prosecuting, Sally O'Neill QC said the girl demonstrated the attack on her to the psychiatrist by using a doll and a toy bear.
By denying rape, the attacker forced the girl into giving video evidence
Defence barristers argued that the child's evidence was not reliable and the allegation could have been suggested to her by another child.
Medical evidence was inconclusive but a test showed a finding which "could be supportive" of the allegation.
Outside court, Det Ch Insp Graham Grant said there was no doubt the girl suffered terribly.
"This case has shocked everyone to the core," he said.
"It is telling that this man denied rape and in doing so forced a young and vulnerable child to endure a daunting criminal process at the Old Bailey."
He described the girl's resilience as "extraordinary".
"I sincerely hope that with continued support of friends and her family she will be able to lead a happy and fulfilled life," he said.
Haringey Council said an investigation into the girl's case was under way, examining the role of different agencies.
Council leader Claire Kober said of Friday's verdict: "We have accepted that things went badly wrong with our child protection in 2007.
"We live every day with the knowledge that more could have been done and apologise again to everyone affected. We are committed to putting things right."
Andrew Flanagan, chief executive of children's charity NSPCC, said the offences were "among the most heinous crimes against small children we have ever seen".
"Thankfully, those responsible have been convicted," he said.
"Hopefully they will receive severe prison sentences which will keep them away from children for a very long time."
Children, Schools and Families Secretary Ed Balls said: "People around the country will be horrified to learn that an adult living in the household of Baby Peter has also committed another vile and disgusting crime against a small and vulnerable child.
"I will not rest until we have implemented the recommendations from Lord Laming, swiftly and thoroughly, so that we can have the best child protection arrangements possible."
DCI Graham Grant: 'There were many lies to conceal the sexual abuse of a toddler'
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