Lewandowski will add the search for a running mate to his day-to-day responsibilities as campaign manager.
The news comes a week after Trump became the presumptive Republican Party nominee and began assigning new responsibilities to close confidantes and top aides as he ramps up planning for the general election.
Lewandowski did not immediately respond to a request for comment.
Trump also said last week that he would be forming a committee to weigh in on potential running mates, one that he said would include his former rival and trusted surrogate Ben Carson, the retired neurosurgeon.
The vice presidential search is still very much in its infancy, a campaign source said, but Lewandowski's assignment means the search will now get underway in earnest.
Trump's decision to put Lewandowski in charge of the search and vetting also marks a break with precedent, as past Republican nominees have typically put a trusted attorney in charge of the vetting process -- not their campaign manager. Although he's among Trump's most trusted aides, Lewandowski is not a lawyer.
Since Trump became the presumptive GOP nominee last week, speculation over his potential running mate has run wild.
Trump has repeatedly said he is looking to tap someone with decades of political experience and relationships in Washington who can help him -- an outsider to the process -- pass his legislative agenda in Congress.
And while Trump has floated some names as possibilities -- including his former rival Ohio Gov. John Kasich -- he has yet to signal who is on his shortlist.
But the speculation has fueled a flurry of responses from potential running mates and party stars, some of whom -- including Florida Sen. Marco Rubio and South Carolina Gov. Nikki Haley -- have said they have no interest in joining Trump on the ticket.
Trump on Tuesday morning fired back at those looking to remove their names from consideration.
"It is only the people that were never asked to be VP that tell the press that they will not take the position," Trump tweeted.
Some, though, have been more receptive, including Oklahoma Gov. Mary Fallin
, who said she would "be very honored if I were to receive a call saying I need you to help make America great again."