Te'o said Tuiasosopo broke the news to him about the prank in a direct message on Twitter on Jan. 16.
An excerpt of the message said, "It's the 16th. I wanted to tell you everything today. I will not say anything to anyone else before I tell you everything. I would and will never say anything bad about you or your family. I completely accept the consequences to the pain I've caused and it's important that you know the entire truth before anyone else."
Teo said he received a call on December 6 from the woman he thought was dead telling him she was alive. Two days later, he spoke about Lennay's death from cancer at a Heisman Trophy ceremony where he was interviewed.
"That's a lie. Why would you say that?" Couric asked.
"Well, at that time, I didn't know," Te'o said. "To be honest with you, I did not know."
"I mean, you knew something," she pressed. "You stuck to the script and you knew that something was amiss, Manti."
"Katie, put yourself in my situation," he said. "My whole world told me that she died on Sept. 12. Everybody knew that. The girl who I committed myself to died on Sept. 12. Now I get a phone call on Dec. 6 saying that she's alive and that I'm going to be put on national TV two days later and to ask me the same question. You know, what would you do?"
Te'o said he worried what everyone he had inspired would think if he hadn't told the truth.
"I did not know who to turn to. I did not know who to tell. I did not know who to trust," he said. "That's the truth. I was just scared, and I didn't know what to do."
He eventually came clean to his parents.
Te'o's parents, Brian and Ottilia Te'o, were also on the show and teared up over their son's efforts to explain himself, including that his biggest regret was lying to his father about Kekua.
"I think the biggest lie that I'm sorry for is the lie that I told my dad," he said. "As a child, your biggest thing is to always get the approval of your parents and for me I was so invested in Lennay and getting to know her that when dad asked me, 'Hey, did you meet her?" I said, 'Yeah.'"
Mrs. Te'o defended her son with a tremor in her voice. She said her son "did exactly what I would expect a responsible, respectable young man to do, to extend himself to someone who said that they lost their father and now they have cancer. I'm proud of his character."
His father, who dwarfed the star football player while sitting next to him, wiped his eyes in praising his son.
"I'm proud of this guy. I really am, and nothing that has happened in the last couple of weeks is going to take that away… I love him. I really do," Brian Te'o said.
"The greatest joy of any child's life is to make your parents proud," Manti Te'o said after a brief pause to compose himself. "The greatest pain is to know they are experiencing pain because of you."
Te'o has struggled with becoming a national punching bag and the butt of many jokes.
"It's been difficult," he said. "Not only for myself, but to see your last name and just to see it plastered everywhere and to know that I represent so many people and that my family is experiencing the same thing. I think that's what was the most hard for me."
In terms of his prior relationship to Tuiasosopo, Te'o said that it is not true that he and Tuiasosopo were family or even family friends.
"Previous to that conversation that he and I had on Jan. 16, I had only talked to Ronaiah twice and he, from my understanding, was Lennay's cousin," Te'o said. "The only time I would talk to Ronaiah was when I couldn't find Lennay."
Watch the full story on "20/20" TONIGHT at 10 ET