Tournament officials confirmed Johnson's entry on Thursday.
"We certainly are excited that Dustin will be joining us in Wilmington in a few weeks," said Wells Fargo Championship tournament director Kym Hougham in a press release. "More importantly, we are glad that he is OK and will be returning to the PGA Tour."
Johnson, 32, injured his back in a fall down a staircase just before the start of the Masters. He warmed up at Augusta prior to the opening round, but decided he could not play.
Johnson had been among the favorites to win the Masters after winning three straight tournaments.
After withdrawing from the Masters Johnson said he planned to take three weeks off.
He has been treating his back with rest as well as riding an exercise bike and performing range-of-motion exercises.