As he made the video address dressed in a black shirt and tie, his girlfriend clutched his arm, a gold-coloured band visible on the ring finger of her left hand.
"I made an incredibly foolish decision and failed those people who trusted and believed in me - most of all, Tasha and our families," Evans added.
"It is a rare and extraordinary privilege to be permitted to play professional football. Now that I've served the custodial part of my sentence of two and a half years, it is my hope that I will be able to return to football.
"If that is possible, then I would do so with humility having learned a very painful lesson. I would like a second chance but I know not everyone would agree.
"I don't believe I have a given right to play again, but for any club to take me on, I've learned a valuable lesson and know that, over time, I can prove myself to be a positive influence, not just on the pitch but also in the community."
Evans was driven out of Wymott Prison in Preston in a Mercedes 4x4 at 5am on Friday amid rumours he had been offered a contract by his old club, Sheffield United, worth more than £500,000 (NZD $1.02 million).
Sheffield United denied the report in The Sun, calling it "false and damaging to the club".
Evans was jailed for five years in 2012 after being convicted of raping a drunken 19-year-old after a former team-mate invited her back to a hotel room in his home town of Rhyl.
He admitted having sex with her, but insisted it was consensual. The woman told the jury she had no memory of the incident.
An online petition against Evans returning to Sheffield United has gained more than 150,000 signatures.
The release of the two-minute video came hours after the BBC was forced to apologise after BBC presenter and veteran journalist Michael Buerk appeared to criticise Evans' victim for being drunk.
In a trailer for Radio 4 discussion show Moral Maze on the rehabilitation of criminals, Buerk said neither footballer Evans nor the woman he attacked emerged "with any credit" because she was so intoxicated "she could barely stand".
His comments have incensed victims' rights campaigners who described the trailer as "damaging" and "deeply offensive".
A Radio 4 spokesman said: "There was no intention to suggest that the victim was in any way at fault, and we apologise if the way this live trail was phrased suggested this.
"Tonight's Moral Maze will ask whether a convicted rapist who maintains his innocence should be entitled to get his job back."
There was also controversy after TV host Judy Finnigan said the disgraced footballer should be allowed to return to Sheffield United.
She and her daughter Chloe both received rape threats online after she told the Loose Women programme the footballer should get his job back.
She had added the victim was "drunk" and the rape was "unpleasant" but "not violent".
Katie Russell, for Rape Crisis England and Wales, said after the BBC controversy today: "To infer that being drunk is in any way 'morally' comparable to committing the serious and violent crime of rape is deeply offensive and will undoubtedly have caused considerable distress to the huge numbers of survivors of sexual violence who will inevitably have been listening.
"Let us not forget that there is a rape survivor at the heart of this story, who is currently living with the devastating and potentially lifelong impact not only of having been sexually violated but of the terrible abuse she has subsequently suffered in the public domain.
"It is partly because of the kind of shaming, victim-blaming attitudes voiced by Michael Buerk this morning that currently only 15 per cent of all those who are raped choose to report to the police."
Ched Evans' full statement
"In May 2011 in a hotel in North Wales, by cheating on my partner Natasha I hurt the woman I love with all my heart.
"Since that night I've constantly regretted my act of infidelity and the damage that has been done on so many fronts because of it.
"The support that's been shown by Natasha, our friends and family during the trial and the time spent in prison has kept me strong.
"It can't have been an easy thing to stand by someone who the court found guilty of such a destructive act. I will be forever grateful.
"Even though I've been released from prison I'm determined to continue to fight to clear my name and it is public knowledge that an application to refer my case back to the Court of Appeal has recently been submitted to the Criminal Case Review Commission by my lawyers.
"The application seeks to demonstrate that the acts I engaged in on that night were consensual in nature and not rape.
"I made an incredibly foolish decision and failed those people who trusted and believed in me - most of all, Tasha and our families.
"It is a rare and extraordinary privilege to be permitted to play professional football.
"Now that I've served the custodial part of my sentence of two and a half years, it is my hope that I will be able to return to football.
"If that is possible, then I would do so with humility having learned a very painful lesson. I would like a second chance but I know not everyone would agree.
"I don't believe I have a given right to play again, but for any club to take me on, I've learned a valuable lesson and know that, over time, I can prove myself to be a positive influence, not just on the pitch but also in the community.
"Thank you for listening to me."
- Daily Mail
