For the first time in more than 20 years, the Democrats have seized full control over the legislature, taking over both Virginia's Senate and the House of Delegates.
However, Mr Beshear, a 41-year-old attorney general whose father was a former governor of the state, said: "We will be ready for that first day in office and I look forward to it".
Beshear's apparent win over Bevin was widely viewed as a humiliating defeat for Trump, who campaigned in Lexington on Monday and pleaded with his supporters to turn out for Bevin.
"This is a close, close race". Bevin has said he would not concede.
Listen Democrats: winning one statewide race against a very unpopular (and unlikeable) incumbent by less than a half percentage point doesn't mean that Kentucky is in play for the general election in 2020.
In Mississippi, Reeves was declared the victor over Democrat Jim Hood for that state's governor's mansion.
To explain Kentucky, Republicans undoubtedly will echo the Trump campaign and focus on Bevin's weaknesses.
The state is often a battleground during presidential elections, and the Democratic result will be seen by many as a blow to Trump's chances next year. Tate Reeves defeated Attorney General Jim Hood, a moderate Democrat who favours gun rights and opposes abortion rights.
The governor expressed great pride and excitement for the state's "extraordinary" achievements in the past four years, -a net increase of almost 93,000 jobs according to the U.S. Bureau of Labor Statistics.
With Washington swept up in the impeachment saga, results in Kentucky, Mississippi and Virginia were closely watched for how the crisis is playing out with voters.
As longtime Kentucky Republican consultant Scott Jennings noted on Twitter Wednesday morning, "For everyone reading the tip sheets this morning on Kentucky, remember - the GOP actually FLIPPED two Dem offices to Republican, and actually controls MORE offices than they did yesterday".
"What we've seen in the Trump era is suburban Republicans are a less reliable Republican vote than rural Democrats, and you can get away with it in states like Kentucky", he said. "You can't let that happen to me!".
Also on that night, he blasted Democrats for recently voting to bring the impeachment probe to a new, public phase.
Instead, the opposite happened.
Beshear maintained his focus throughout the race on "kitchen table" issues like health care and education to blunt Bevin's efforts to hitch himself to Trump and nationalize the race.
Republicans '[w] on 5 out of 6 elections in Kentucky, including 5 great candidates that I spoke for and introduced last night, ' the president tweeted.
"We need moral leadership that seeks to unite this country and work for a better future for all Americans".