Both the columnist and her younger brother Jo Johnson, the universities minister, supported the remain campaign in the July referendum.
Ms Johnson has defected from the Tories to the Liberal Democrats because they “have the only sensible plan in place”.
She added that leaving the European Union is a “suicide mission” that will take Britain “over a cliff”.
Writing in the Mail on Sunday, Ms Johnson said her eldest sibling “made it quite clear he thought I’d lost my last remaining marble” when she confessed she was now a paid-up member of the opposition.
Explaining her decision, she wrote: “As I say to my brother every time I see him – and he would, I hope, admit I’ve been consistent if not loyal on this – the reason I’ve gone as far as to join an opposition party is because the goods the Brexiteers showed us in the referendum bill of sale have so far turned out to be faulty.”
Ms Johnson highlighted how, after assurances by US officials that Britain would be “front of the queue” for a trade deal, Britain is now “behind the EU”.
She said the promise of £350 million in funding for the NHS, which was scrawled across her brother’s Brexit bus, is no more, migration will have to remain at current levels in order for the country to thrive, and growth is slowing.
“And on it goes – and Brexit hasn’t even happened yet. And therefore for me, this time round, the only way is the Lib Dems,” Ms Johnson added.
There was speculation that Ms Johnson was poised to stand as a Lib Dem candidate in the June 8 General Election, however she said it “can’t and won’t happen” due to “rules and procedures”.
Accepting responsibility for any fallout over her “defection from the political family fold”, she wrote: “I could have told nobody I’d joined the Lib Dems.
“I could have merely shown my allegiance in the privacy of the voting booth, but I didn’t.
“I wanted to stand up and be counted in my continuing opposition to what I’ve always thought is a suicide mission to take us out of Europe and over a cliff.”