Markell, appearing at his campaign headquarters shortly before 9:30 p.m., told The Associated Press that Carney had called him and conceded the race.
Markell says Carney "was a class act" and "very gracious."
Retired Superior Court judge Bill Lee earned his second shot at the governor's office Tuesday, easily defeating airline pilot Michael Protack to win the Republican gubernatorial nomination.
With 15 of 339 precincts reporting, Lee had 1,241 votes, or 71.6 percent, compared to 492, or 28.4 percent, for Protack.
Lee narrowly lost the GOP nomination in 2000, but he defeated Protack in a primary four years ago and went on to almost upset incumbent Democrat Ruth Ann Minner. As he did in 2004, Lee refused to debate Protack during the primary campaign this year.
Protack, a perennial candidate who has lost two bids for the GOP gubernatorial nomination and waged a brief primary campaign for U.S. Senate in 2002, has criticized state GOP leaders as being ineffective, but he has attracted little support or fundraising from party members.
Two other races of note in Delaware:
In the Democratic race for congress, Karen Hartley-Nagle beat Michael miller and Jerry Northington.
Hartley -Nagle will face Republican incumbent Mike Castle in November.
In the race for Mayor of Wilmington, Democratic incumbent James Baker has easily defeated challenger Robert Bovell, Jr.
Baker faces no Republican opponent this fall.
He will become the first mayor of Wilmington ever to serve three terms.