The home secretary said Mr Johnson is “better placed” than Jeremy Hunt to “deliver what we need to do at this critical time”.
The former Tory leadership hopeful is now the most senior cabinet member to endorse Mr Johnson.
He is rumoured to be positioning himself as the frontrunner’s future chancellor.
In a speech on Tuesday, Mr Javid is expected to declare plans for an “emergency budget” to boost the economy in the event of a no-deal Brexit, according to The Sunday Times.
He will reportedly say: “Trust in our democracy will be at stake if we don’t make October 31 a ‘deal or no deal’ deadline.
“To prepare that, we are agreed on the need for ramped-up no-deal preparations, including a budget.”
Mr Johnson has insisted he is not bluffing over his commitment to take the UK out of the EU on October 31, with or without a deal.
His challenger Jeremy Hunt has said he is also prepared to leave without a deal, but has warned it would not be the most secure way of guaranteeing Brexit because MPs would try to block it.
The Sunday Times also revealed that Mr Johnson could call a general election at the start of September to win a new mandate before the October 31 Brexit deadline.
He has not ruled out proroguing parliament if necessary.
However, current chancellor Philip Hammond has privately warned that Mr Johnson would “crash the pound” if he pursued a no-deal departure.
He told the BBC he and other MPs would “find a way” of blocking a no-deal Brexit.