Inslee will replace outgoing Gov. Christine Gregoire after McKenna acknowledged he could not overcome the estimated 41,000 vote deficit he faced as of Friday evening, The Seattle Times reported.
McKenna called Inslee just before 6 p.m. to congratulate him on his victory.
Inslee, a former eight-term U.S. representative, is the eighth consecutive Democrat elected as governor of the Evergreen State.
"In a year like this we were trying to swim up against a 12-and-a-half or 13-point tide at the top of the ticket, and that's problematic," McKenna campaign manager Randy Pepple said.
U.S. Sen. Maria Cantwell, D-Wash., won re-election Tuesday, and Washington voters also approved measures to legalize marijuana and same-sex marriage.