The photo was taken in Edinburgh in 2007 as fund-raiser Savile and the cardinal unveiled a £375,000 vehicle for the disabled.
The pair first met in the 70s, when O’Brien was a priest in Kilsyth, North Lanarkshire – and worked with a friend of Savile’s mum.
Another priest at Kilsyth at the time has been suspended following claims of abuse against two young victims.
It was Cardinal O’Brien who ordered the investigation last September.
When Savile’s vile secrets became known, the cardinal called for him to be stripped of his papal knighthood, awarded in 1990.
Cardinal O’Brien quit just 24 hours before he was due to fly to Rome to help choose the next pope.
He stepped down with immediate effect amid accusations of “inappropriate acts” towards fellow priests – claims he strongly denied.
The controversial cleric said he did not want the scandal surrounding him to overshadow the papal election.
His resignation followed a series of recent allegations against him dating back to the 80s by three priests and one former priest.
The ex-priest claimed the cardinal made an inappropriate approach after night prayers at St Andrew’s College, Drygrange.
Another said he was living in a parish when he was visited by O’Brien, and inappropriate contact took place.
A third accused him of “unwanted behaviour” after late-night drinking.
And a fourth alleged he used night prayers as excuse for inappropriate contact.
Yesterday it emerged Pope Benedict had accepted O’Brien’s resignation a week ago.
The cardinal, Archbishop of St Andrews and Edinburgh, said in a statement: “I have valued the opportunity of serving the people of Scotland and overseas in various ways since becoming a priest.
“Looking back over my years of ministry, for any good I have been able to do, I thank God. For any failures, I apologise to all whom I have offended.”
The cardinal, who missed celebrating mass at St Mary’s Cathedral in Edinburgh on Sunday, had been due at the Vatican today to join the conclave to elect Pope Benedict’s successor.
Only a few days ago he appeared on TV showing the ballot paper he would be using.
His sudden departure means Britain will be unrepresented in the process as he was the only cardinal in the British Catholic churches.
Announcing his decision not to take part, he said: “I do not wish media attention in Rome to be focused on me – but rather on Pope Benedict XVI and on his successor.
"However, I will pray with them and for them that, enlightened by the Holy Spirit, they will make the correct choice for the good of the Church.”
O’Brien, who was made a cardinal by Pope John Paul II in 2003, tendered his resignation in November citing “indifferent health”.
But he had not been expected to step down until his 75th birthday on March 17.
Scotland’s first minister Alex Salmond said yesterday: “In all of my dealings with the cardinal, he has been a considerate and thoughtful leader of the Catholic church in Scotland, stalwart in his faith but constructive in his approach.”
Mr Salmond said it would be a “great pity if a lifetime of positive work was lost from comment in the circumstances of his resignation.”
He added: “None of us know the outcome of the investigation into the claims made against him but I have found him to be a good man for his church and country.”
Jack Valero, of lobby group Catholic Voices, said it was right for Cardinal O’Brien to resign.
He said: “I am very happy that this has been taken seriously, that the nuncio – the Pope’s representative in the UK – has written to the four people who have made the allegations to thank them for speaking out, and that the whole thing has been done so quickly.
"I think this shows a new spirit.”
Cardinal O’Brien, who – along with Prince Philip – welcomed Pope Benedict to Scotland in 2010, was no stranger to controversy.
He recently clashed with the Scottish government over its plans to enshrine same-sex marriage in law by 2015.
A year ago he described gay marriage as a “grotesque subversion of a universally accepted human right”.
His uncompromising stance led to him being named Bigot of the Year by gay rights group Stonewall Scotland.
Stonewall director Colin Macfarlane said: “We hope his successor will show a little more Christian charity towards openly gay people.”
Born in Ballycastle, County Antrim, on St Patrick’s Day, the cardinal was ordained in 1965 and became Archbishop of St Andrews and Edinburgh 20 years late.
He has also been an outspoken defender of Catholic teaching on abortion and euthanasia.
Six years ago he claimed the abortion rate in Scotland was equivalent to “two Dunblane massacres a day”.
And in another outspoken attack, he described the implications of the Human Fertilisation and Embryology Bill as akin to “Nazi-style experiments”.