Pence's announcement comes after several weeks of deliberations, featuring several candidates, an administration official said, adding that no taxpayer money will be used.
In May, President Donald Trump hired his own special counsel - his longtime lawyer Marc Kasowitz - to help represent him in the ongoing probe into possible Russian interference. Cullen also previously served as Virginia's Attorney General in the late 1990s.
The lawyer, Richard Cullen, is a former Virginia attorney general and a former United States attorney for the eastern district of Virginia. Paul Trible, R-Va., during the Iran-Contra investigation, worked for former Rep. Caldwell Butler, R-Va., during the Watergate investigation, was lead counsel to former House Majority Leader Tom DeLay during the investigation into his ties with lobbyist Jack Abramoff and was on President George W. Bush's legal team during the Florida recount in the 2000 presidential election. Richard Cullen has a long record as a high-profile attorney in Washington, particularly in Republican circles.
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The probe, which began previous year as an investigation into Moscow's meddling in the presidential election, has since widened to include prospective money laundering by Trump associates and the possibility that people close to the President were in contact with Russian operatives throughout the campaign.
The president denies doing anything wrong and has called the investigations a "witch hunt".
Comey testified last week that the President demanded loyalty and pressed him to drop a probe into disgraced ex-national security adviser Michael Flynn.
But obstruction came into play after Trump fired Federal Bureau of Investigation director James Comey last month.
According to his McGuireWoods bio page, Cullen is "frequently called on to conduct confidential internal investigations to assist corporations in assessing the risk of criminal prosecution or regulatory enforcement".