If confirmed by the Senate, James Comey will replace outgoing director Robert Mueller III, serving for 10 years.
At the White House, Mr Obama praised Mr Comey as a model of "fierce independence and deep integrity".
Mr Comey is known for successfully opposing a warrantless wiretapping programme backed by other Bush aides.
Mr Mueller took up his post shortly before the 9/11 attacks and is retiring as director on 4 September.
In remarks on Friday, Mr Obama said the outgoing director had displayed "a steady hand and strong leadership" during his time at the head of the FBI.
The US president said Mr Comey had "law enforcement in his blood".
"As a young prosecutor in the US attorney's office in Manhattan he helped bring down the Gambino crime family; as a federal prosecutor in Virginia he led an aggressive effort to combat gun violence that reduced homicide rates and saved lives," Mr Obama said.
He also joked that Mr Comey - who is 6ft, 8in tall (2.03m) -  was "a man who stands up very tall for justice and the rule of law".
The nominee said he could not describe his excitement to work again with the FBI.
"They are men and women who have devoted their lives to serving and protecting others and I simply can't wait to be their colleague," he said.
One of the most dramatic episodes of Mr Comey's tenure as deputy attorney general in the Bush administration came in 2004, when then-Attorney General John Ashcroft was ill in hospital.
Mr Bush's White House counsel Alberto Gonzales and Chief of Staff Andrew Card pressed him in his hospital bed to re-authorise a controversial programme allowing federal agents to eavesdrop on phone conversations without a warrant.
Mr Comey, who was acting as attorney general in Mr Ashcroft's stead, rushed to the hospital and intervened.
Changes were subsequently made to the programme and Mr Comey drew wide praise.
Mr Obama alluded to the incident on Friday, saying Mr Comey "was prepared to give up a job he loved rather than be part of something he felt was fundamentally wrong".
After leaving the Bush administration, Mr Comey was general counsel for Bridgewater Associates, a hedge fund in the US state of Connecticut. He now lectures at Columbia University law school in New York.
Before he became deputy attorney general, Mr Comey had a long tenure at the justice department, serving in many posts including as US attorney for the Southern District of New York.

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Guy, 20, took third behind winner Dutchman Sebastiaan Verschuren in the 200m freestyle after missing out on the men's 400m final.
Tutton, 19, claimed bronze in the 100m women's breaststroke race won by world record holder Ruta Meilutyte.
"That race was amazing," Tutton told BBC Sport. "I'm just over the moon."
Meilutyte triumphed in one minute 6.17 seconds, ahead of Iceland's Hilda Luthersdottir.
The Plymouth-based Lithuanian was winning back at the pool where she took the 2012 Olympic title aged 15.
Tutton edged out Irish swimmer Fiona Doyle for third in 1:07.50, with Tutton's team-mate Molly Renshaw in seventh.
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In the 200m freestyle, Verschuren won gold in a time of 1:46.02, with Serbia's Velimir Stjepanovic second in 1:46.26 and Guy finishing in 1:46.42.
"For me, that was a great swim and a season's best," said Guy. "Rio is going to be a real scrap to the finish line."
Britain's Max Litchfield and Dan Wallace were seventh and eighth in the men's 200m individual medley final won by Greece's Andreas Vazaios.
Scot Ross Murdoch breezed through to Thursday's 200m breaststroke final with a winning time of 2:09.72.

North Wales Police said the incident involved just one vehicle on the B5111 in Coedana, Llanerchymedd at about 17:30 BST.
The road has been closed and diversions are in place.
Two police officers are being treated for minor injuries at Ysbyty Gwynedd in Bangor.
US President Barack Obama has nominated a former justice department official under President George W Bush as the next FBI director.
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England's James Guy and Welsh swimmer Chloe Tutton won bronze medals at the European Championships in London.
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A police car has crashed while responding to an emergency call on Anglesey.