Sudan's President Omar al-Bashir pardoned her after a meeting with two British Muslim peers.
In a statement, Mrs Gibbons said "I am sorry if I caused any distress". Gordon Brown said he was "delighted and relieved" at the news.
She said she was in "total shock" but was "well treated in prison and everyone was very kind to me".
Mrs Gibbons' son and his girlfriend were at Heathrow Airport to greet her.
She arrived back to London via Dubai, accompanied by British Muslim peers Baroness Warsi and Lord Ahmed, and is said to have slept for much of the journey.
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