Lord Frost resigned with “immediate effect” on Saturday night, having previously agreed with the prime minister he would leave his job in January.
Citing “the current direction of travel” of the government, as well as fears over “coercive” Covid measures and the wish for the UK to become a “lightly regulated, low-tax” economy, Lord Frost’s departure was described as a “watershed moment” in what had been an extremely damaging week for the PM.
Downing Street said Ms Truss would take over ministerial responsibility for the UK-EU relationship, and would lead negotiations to resolve issues with the Northern Ireland Protocol.
Ms Truss underwent a transformation from being pro-Remain to an avid Brexiteer following the referendum in 2016.
She consistently polls as the most popular Cabinet minister with Tory members, and has been tipped as a future leadership contender.
Meanwhile, Chris Heaton-Harris will move from the Department for Transport (DfT) to become Europe minister and will deputise for Ms Truss when needed.
Aldridge-Brownhills MP Wendy Morton will move from being Europe and Americas minister to replace Mr Heaton-Harris at the DfT.
European Commission vice-president Maros Sefcovic said he hoped to continue negotiations with Ms Truss in the “same constructive spirit”.
He tweeted: “I take note of the appointment of @trussliz as co-chair of the Joint Committee and Partnership Council.
“My team and I will continue to cooperate with the UK in the same constructive spirit on all important tasks ahead, including the Protocol on Ireland/Northern Ireland.”
It comes after Lord Frost’s shock resignation piled more pressure on the Prime Minister.
Senior Tory MP Tobias Ellwood (Bournemouth East), who chairs the Commons Defence Select Committee, said many Conservative colleagues shared Lord Frost’s desire for there to be “a consistency of where we want to go”.
He told Times Radio: “I think this is what perhaps unites more and more of the wider party, and we’ve seen this since the Owen Paterson debacle, is that it needs to be clarity of our vision, there needs to be a consistency of where we want to go, people need to be included, the decision-making in No 10 needs to be improved.
“We need an, almost like, a wartime leader, we need a strong No 10, and the machinery of No 10 around Boris Johnson, that’s what needs to be improved.
“The boosterism, the energy, is not enough in these current circumstances alone.”
Peter Bone, MP for Wellingborough, told ‘Trevor Phillips On Sunday’ on Sky News: “Boris has led this country exceptionally well – but what comes next? And that’s what I think Lord Frost is talking about.
“I think part of that rebellion of 100 Conservative MPs was partly due to the fact that we want to see the prime minister move to a more conservative agenda in future.”
Mr Bone also said he agreed with Lord Frost’s concerns over the prospect of “coercive measures” to control coronavirus.
The MP said: “I’ve cancelled all in-person meetings and the get-together with staff, I cancelled.
“I won’t be going to crowded places, but leave that up to the individual to make that decision, don’t have the state telling me what I have to do every day, and so in that regard, yes, I’m with Lord Frost on that.”
Meanwhile, chairman of the Northern Ireland Affairs Committee, Simon Hoare, told BBC Radio 4’s ‘The World This Weekend’ that the issues cited by Lord Frost were the same that had been raised by “at least one potential leadership candidate”.
And he said: “I do just wonder whether he’s acting as a bit of an outrider for them, I’m just not sure.”