The Stamford Advocate reported Simmons called McMahon to concede shortly before 10 p.m. EDT. Peter Schiff, a financial commentator, was running third.
"I essentially have endorsed her tonight by pledging my support to her," Simmons said when asked if he would endorse McMahon. "In some areas we've agreed, in others we've disagreed, but that's what campaigns are all about. Now is not the time to continue the conflict."
McMahon, former chief executive officer of World Wrestling Entertainment, spent more than $22 million of her own money on her primary campaign. She will go head-to-head against Democrat Richard Blumenthal, the longtime state attorney general in the November election. The winner will succeed Sen. Christopher Dodd, a Democrat.
"This election is about jobs," McMahon said following her primary win. "The American Dream is threatened, but Washington continues its reckless spending, massive debt, and tax increases. Washington is suffocating small businesses and killing jobs. This is not only threatening our well-being, but also the well-being of our children and grandchildren. It's time for something different."
Stamford Mayor Dannel Malloy defeated businessman Ned Lamont for the Democratic nomination to become Connecticut's next governor. On the GOP side, former U.S. Ambassador to Ireland Tom Foley had 43 percent of the vote to Lt. Gov. Michael Fedele's 37 percent and businessman Nelson "Oz" Griebel's 20 percent with about 54 percent of the precincts counted.
Outgoing Republican Gov. M. Jodi Rell chose not to run again.