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According to this Google search the first appearances of this text on the internet is in 2001.
And (among those earliest references) this says,
Actually, the origins of this prayer are unknown. Sylvia Boorstein shared with me that she learned a prayer almost exactly like this one—a Jewish prayer—as a child.
I think that may be right -- it seems to me similar in structure to the Serenity Prayer, for example.
Also I think that "forgiveness" doesn't show up as a major theme in the Pali canon (but it's central to Christianity, e.g. "the forgiveness of sin"). This search doesn't return many results.
Reconciliation, Right & Wrong explains a difference between forgiveness and reconciliation -- to the extent that they do talk about reconciliation, I think that's mostly in a monastic (community) context, and along the line of confessing one's own transgression and admitting a fault, to avoid repeating the mistake: and I think you'd do that in person i.e. say it to someone else, not say it silently in prayer.
The other side of the coin that is promoted in the sutta is the Akkosa Sutta, where an insult isn't forgiven because it isn't accepted.
And Wikipedia's article about Forgiveness (which talks about "reliious views" of forgiveness, starting with Judaism) says,
Buddhism places much emphasis on the concepts of Mettā (loving kindness), karuna (compassion), mudita (sympathetic joy), and upekkhā (equanimity), as a means to avoiding resentments in the first place.
The one kind of Buddhist text that this does remind me of is the Metta Gatha.
By Googling for khama gatha I found some slighty similar texts, for example in this Gatha Book:
ASKING FOR FORGIVENESS ( KHAMA YACANA)
Kayena vaca-cittena Pamadena maya katam
Accayam khama me bhante Bhuripanna tathagata.If, due to neglence, I have done some wrong by body,speech, or mind
Forgive me of that offence, O Bhante, Perfect One of vast wisdom.
... and these Daily Buddhist Prayers:
Rectification of faults
Kāyena vācā cittena
Pamādena mayā katam
Accayam khama me bhante
Bhuri pañña TathāgataKāyena vācā cittena
Pamādena mayā katam
Accayam khama me dhamma
Sanditthika akalikaKāyena vācā cittena
Pamādena mayā katam
Accayam khama me Sangha
Supatipanna anuttara
Sadhu! Sadhu! Sadhu!If due to negligence I have done
Some wrong by body, speech, or mind.
Pardon me that offence, Bhante!
Perfect One of vast wisdom.If due to negligence I have done
Some wrong by body, speech, or mind.
Pardon me that offence, O Dhamma
Visible and immediately effective.If due to negligence I have done
Some wrong by body, speech, or mind.
Pardon me that offence, O Sangha
Practising well and supreme.
Excellent! Excellent! Excellent!
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As far as I know there are no prayers for Forgiveness: we should know about good and bad, we should try to do good and avoid the bad.
Instead of, "If I have harmed anyone in any way either knowingly or unknowingly", it would be better to apologise and remember your fault and don't do it again, and try to follow 5 rules.