Richard Cullen is known for representing high profile clients.
Earlier, US media reported that Donald Trump was being investigated by special counsel Robert Mueller for possible obstruction of justice.
Mr Mueller is leading an FBI inquiry into Russia’s alleged meddling in the 2016 presidential election.
Reports in US media said senior intelligence officials would be interviewed on whether Mr Trump tried to end an inquiry into his sacked National Security Adviser Michael Flynn, and about the firing of FBI chief James Comey.
Mr Trump – who has repeatedly denied any collusion with Russia – said the move was the latest action in a “phony story”.
“You are witnessing the single greatest WITCH HUNT in American political history – led by some very bad and conflicted people!” the US president tweeted.
Mr Pence’s office announced the decision to hire Mr Cullen on Thursday. It said the vice-president had earlier interviewed several candidates.
“The vice president is focused entirely on his duties and promoting the president’s agenda and looks forward to a swift conclusion of this matter,” Mr Pence’s spokesman Jarrod Agen said.
Mr Cullen is the chairman of McGuireWoods LLP law firm.
He represented high profile clients such as former US congressman Tom DeLay and Elin Nordegren, ex-wife of golfer Tiger Woods.
He was also involved into the Iran-Contra and the Watergate investigations.
Last month, President Trump hired his own lawyer, Marc Kasowitz, to handle Russia-related investigations by the FBI and US congressional committees.
Why is President Trump reportedly being investigated?
The latest media reports say the obstruction of justice investigation began just days after Mr Trump fired Mr Comey on 9 May.
Mr Comey, who had been leading one of several Russia inquiries, testified to Congress last week that the president had pressured him to drop the inquiry into Mr Flynn.
Mr Flynn stepped down in February after failing to reveal the extent of his contacts with Sergei Kislyak, the Russian ambassador to Washington.
Mr Comey testified under oath that Mr Trump had told him during a private meeting: “I hope you can see your way clear to letting this go, to letting Flynn go. He is a good guy. I hope you can let this go.”
The White House has said the president “has never asked Mr Comey or anyone else to end any investigation, including any investigation involving General Flynn”.
Mr Comey said he was “sure” Mr Mueller was looking at whether Mr Trump had obstructed justice.
But Mr Comey also testified that to his knowledge the president had not tried to stop the Russia investigation.
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Source: BBC