Gartside's proposal is expected to be discussed at a meeting of Premier League clubs this week and Redknapp has become the first English boss to publicly back the concept.
He told the Daily Record: "Absolutely, I would welcome Celtic and Rangers to English football if they wanted to play down here. No doubt about it. I'm sure they would be good for the English game.
"We are talking about two huge football clubs and if they were to join our league you would be looking at great games in great stadiums.
"I was up in Scotland only a couple of months ago to watch Celtic play Arsenal in the Champions League qualifiers and the atmosphere was out of this world.
"It was incredible and I'd love to see games like that on a more regular basis.
"The one worry I would have is what happens to the rest of Scottish football if the two of them are allowed to leave but only the people up there know the answer to that.
"If you're asking me if it would be good for the English game then the answer is yes."
Former Celtic player Moyes and ex-Parkhead boss O'Neill have emotional ties to their former club but Redknapp is a more dispassionate observer.
And despite acknowledging the Old Firm would eventually become a threat to his own club, he would still welcome them with open arms.
He said: "It's true, with the extra money they would get down here the two of them probably would end up challenging clubs such as ourselves for European places but that's nothing something we should be scared of.
"We are talking here about two great clubs and it would be fantastic to compete against them. It would only make the game in this country stronger if we had two clubs with their tradition operating in our league."