Q. Is it necessary to tell or communicate in any form or way to the person who has offended you that he is forgiven?
A. My seminary rector once asked me, “What are the 3 theological virtues?” I responded, “Faith, hope and charity.” He then asked me, “And which is the greatest?” I replied, “Charity?” He said, “Nope, prudence!”
Along the same lines, this may be the best way to approach communicating forgiveness to another person. What is absolutely necessary is that the sin be confessed to God in the Sacrament of Reconciliation. It is here that you will be absolved of this sin and, hopefully, a priest will give you some prudential judgment as what to do next.
It may be that it will be beneficial to you and to those you offended to approach them and tell them you forgive them or ask for their forgiveness. Perhaps this will be done in person, via phone call, email, text, etc. But, there may be circumstances that will make a direct face to face “I’m sorry or I forgive you” not possible. Maybe the person has died, maybe they are in prison and visiting them would be imprudent, maybe saying it to their face would cause them to want to kill you, etc. It is prudent to ask the advice of your confessor what needs to be done to make right the sin that you have committed.