Talks over Warnock's future took place after the 2-0 win over Manchester United on Monday (AEST) and an agreement has been reached for him to remain at the helm.
The Bluebirds looked like defying the expectations of many in their single season back in the Premier League, but a 3-2 defeat to Crystal Palace in the penultimate round of fixtures resulted in its relegation.
Warnock, 70, now has the chance to build on his record of eight Football League promotions, achieved when he guided the club to a top-two finish in the second tier in 2017-2018.
"He is the best man for the job, there was never any doubt in my mind," Dalman said.
"We all share the same vision. We will give [promotion] another go."
Former Sheffield United and QPR boss Warnock dismissed the possibility of overseeing another Premier League campaign when asked about his future after the season-ending triumph at Old Trafford.
"I wouldn't want to manage in the Premier League again," he said.
Cardiff finished two points adrift of safety in the top flight, having won 10 and drawn four of its 38 matches.