Lord Frost resigned on Saturday night, citing the Government's "current direction" and "coercive" Covid measures.
Boris Johnson had a disastrous week and his sudden departure was hailed as a ‘watershed moment'.
‘Boris has led this country exceptionally well – but what comes next?' said veteran Tory MP Peter Bone.
‘I think Boris Johnson is the best person to take us through the challenges the country faces,' Sajid Javid said on Sunday.
Ms Truss will lead negotiations to resolve issues with the Northern Ireland Protocol, according to Downing Street.
Following the 2016 referendum, Ms Truss went from Remainer to ardent Brexiteer.
She is the Tory Party's most popular Cabinet minister and a future leadership contender.
The Liberal Democrats claim this was her motivation.
‘The Tories are breaking themselves apart under Boris Johnson,' said Layla Moran. The PM is more concerned in destroying his political opponents than doing what is best for the country. Liz Truss has often demonstrated that she is mainly concerned with appealing to Conservative party members. It's a shame.'
Vice-President Maros Sefcovic said he hoped to continue talks with Ms Truss in the same spirit.
On all important tasks ahead, including the Protocol on Ireland/Northern Ireland, my team and I will continue to work constructively with the UK.