Mr Carlaw said it would be “far more damaging” to continue with the “endless drift”, and said he would back the Prime Minister in leaving the EU on 31 October, even if there was no deal agreed with Brussels.
It comes just two months after Ms Davidson, who resigned as Scottish Tory leader in August, said her party “won’t support” a no-deal Brexit.
Asked about the change of policy, Mr Carlaw said: “Ruth has got very firm views. Everybody has views on Brexit.
“My preference is for a negotiated way out. It always has been. But I’m not someone who has argued that the roof will fall in on the world in an alternative scenario if we have properly prepared for it.
“I think the effort now to properly prepare for it is underway. There are a whole series of other agreements that will apply irrespective of whether we come out of the European Union with the broader comprehensive deal that we all want to see happen.
“Far more damaging is the endless drift, three years after we voted, three years of businesses not knowing whether they’re going to end up.
“Another six month extension does not guarantee that anything will be any different at the end of it. At some point you have to say, we have to move on, and I think we are at that point now.”
Writing in July, Ms Davidson said: “When I was debating against the pro-Brexit side in 2016, I don’t remember anybody saying we should crash out of the EU with no arrangements in place to help maintain the vital trade that flows uninterrupted between Britain and the European Union.
“I don’t think the government should pursue a no-deal Brexit and, if it comes to it, I won’t support it.”