King broke the shock news at the Ibrox club's AGM on Tuesday that he plans to give up his boardroom role in the new year. But he will remain as Gers' major shareholder and that is music to Gerrard's ears.
Speaking ahead of Thursday's Europa League showdown with Feyenoord, the Ibrox boss said: "I met Dave on Saturday night, we had dinner together, he told me about his decision.
"I've got massive respect for Dave and the job he's done chairing the board.
"The positive thing is he's not going anywhere. He'll still be a shareholder. Still be about. I think it's important that I've got that relationship.
"Dave is somebody that I trust very much. He's given me fantastic support."
Gerrard added: "[King] was big influence on my decision to come here in the first place.
"The main thing that came out of meal was the relationship won't change. He'll still be there for me. That's very important.
"The relationship has been as close as it needs to be. We always spend some hours together, when he's over, talking about the team, individual players, the progress.
"We always have a review of where we're at. That won't change. We'll continue to sit down when he comes over. I've got contact into him whether it be email or phone. He's always been very quick to respond and always been there for me from day one.
"The very pleasing for me is that won't change."
Rangers can take a major step towards booking a last-32 slot if they overcome Dick Advocaat's team at De Kuip on Thursday evening.
They also have a Betfred Cup final showdown with Celtic to look forward to next month but Gerrard does not believe the outgoing chairman's legacy should be measured in wins and losses.
He said: "I don't think the games moving forward will impact his legacy. You saw the reaction at the AGM and the reaction since the news.
"He deserves that. He reluctantly went into that role in the first place, he's given five years of his life to it and dedicated it to Rangers to put it in a better position than when he took over.
"I've got nothing but admiration and respect for him from a personal point of view having got to know him. He's a good guy, a good type who cares about this club and its supporters.
"I'm sure the club and board will continue to move forward. And it's important that he's staying."