Ross begins tonight's 'Friday Night with Jonathan Ross', which was recorded on Wednesday afternoon, with the words: "So where were we?".
In his opening monologue he pokes fun of the verbal gaffes of former US president George W Bush, which leads into a dig at himself. He says: "What kind of idiot would say stuff like that knowing it would be broadcast?"
Ross then becomes serious and apologises for the obscene phone messages that he and comedian Russell Brand left for Sachs about his granddaughter Georgina Baillie while broadcasting Brand's former Radio 2 show.
Ross says: "There can't be many watching who aren't aware that this show hasn't been on recently and the reason for its absence. Well, I am going to take this opportunity to apologise for what I said on the radio.
"Being on the BBC and being allowed this level of freedom to communicate openly with people is a great privilege and something I've always enjoyed and I value enormously.
"In future I do intend to be more aware of the responsibility that comes with such a gift. But as the kids say, it was my bad, so I do apologise for any hurt or distress it's caused."
Throughout the programme Ross makes short references to the incident, including joking that for the past three months he had been "sitting on the sofa eating crisps".
Tom Cruise, who was in London to promote his latest movie 'Valkyrie', appears as Ross's final guest on the show. The comedians Lee Evans and Stephen Fry also appear.
It is thought as both have become avid users of the microblogging service.
Ross was suspended without pay on October 30 last year after thousands complained about the phone messages, in which Ross told Sachs that Brand "fucked" his granddaughter.
Brand resigned from his Radio 2 show shortly after the incident and was later followed by Radio 2 controller Lesley Douglas and David Barber, the station's head of specialist music and compliance.
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