The BBC arts presenter and executive was been cleared of abusing expenses after a three-month internal inquiry, authorised by Thompson.
Yentob, who is the BBC's creative director and head of drama, entertainment and children's programmes, was alleged to have used chauffeur-driven cars and received upgrades on flights using the BBC's expense budget.
Thompson said on clearing Yentob today: "I am satisfied that there has been no dishonesty on Alan's part.
"I am also satisfied, on the basis of the evidence, that Alan's reputation for honesty and integrity in his work is fully justified."
The inquiry did suggest, however, that Yentob had taken insufficient care over some aspects of his affairs at the BBC. Yentob has agreed to correct this and to ensure the timely and effective administration of all his affairs.
Thompson added that it was in everyone's interest, including Alan's, that the allegations should be investigated thoroughly.
"Nonetheless I regret that Alan has had to endure a great deal of unfair press speculation during the process.
"I hope that he and we can now put this matter behind us and that Alan can focus all his energies on his task as one of the BBC's key creative leaders."
The allegations were investigated by the BBC's chief operating officer John Smith at the request of Thompson in July this year.
Yentob dismissed the claims as a "whispering campaign" by a disgruntled colleague or colleagues and has continued to work for the corporation during the inquiry.
The former BBC director-general Greg Dyke confirmed a £20,000 bonus to Yentob and said: "I have always been a great fan of Alan's. Last year, I recommended he receive a special bonus because of all the additional work he put in when 'Imagine' was created."
Yentob first faced criticism back in 2002 when he hosted a Glastonbury party at his mansion in Somerset with BBC money. The corporation defended Yentob and said the party was an appropriate event to stage because it televised the music festival.
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