The South West Norfolk MP defeated former chancellor Rishi Sunak, taking 57 per cent of the vote to Mr Sunak's 43 per cent, when the results of the long-running leadership election were held yesterday.
She is set to formally succeed Mr Johnson today.
Miss Truss's election has been welcomed by Shropshire's Tory MPs, but they warned there was a lot that needed to be done.
And Labour and Liberal Democrat leaders in the county said Miss Truss did not represent the change in direction the country needed.
Tory MP for Shrewsbury and Atcham, Daniel Kawczynski, had backed Miss Truss in the contest, and said he was delighted she had won.
He said: "She has the backbone and steel to do what is required in this particularly difficult time for our nation."
Mr Kawczynski said she needed to act swiftly to provide support for small businesses and families struggling with the cost-of-living crisis.
"The pub trade is facing terrible challenges with soaring energy prices," he said.
"Many small businesses have been badly affected by the energy spike."
Mr Kawczynski said Miss Truss was right to say borrowing would need to increase to provide immediate support to deal with rising costs.
The other priority should be a long-term strategy to increase productivity through deregulation, he added.
"We want to see a Brexit bonus in terms of getting rid of regulations and red tape," he said.
Mark Pritchard, MP for The Wrekin, said he was delighted by the result: "Strength and tenacity are needed in times of great challenge. She has these vital attributes."
Philip Dunne, MP for Ludlow, congratulated Miss Truss on her election
"I look forward to the party getting behind her to give the country the first-class leadership it needs," he said.
Mr Dunne said tackling energy bills should be an urgent priority.
He said action needed to be taken on energy bills this month, before they potentially quadrupled in October.
Clwyd South MP Simon Baynes, who like Mr Dunne had backed Mr Sunak, congratulated Miss Truss on her election. "I look forward to strongly supporting our new Prime Minister in her vital work ahead.”
North Shropshire Liberal Democrat MP Helen Morgan dismissed Miss Truss as a 'new prime minister, same old government'.
"Truss has shown her true colours by admitting she does not support taxing the super-profits of oil and gas giants," said Mrs Morgan.
Jane Dodds, leader of the Welsh Liberal Democrats, added: "Under Liz Truss we are set to see more of the chaos that we saw under Boris Johnson.
"The Conservatives have shown they don’t care, have no plan and have failed our country," said Mrs Dodds.
Councillor Shaun Davies, leader of Telford & Wrekin Council, said it would be up to Miss Truss to repair the 'damage' caused by previous Conservative-led governments over the past 12 years.
"After six weeks of talking to themselves, the Conservatives Party has got to come forward with a plan to tackle the cost of living," he said.
"There should be a general election to see which prime minister people prefer – Liz Truss or Keir Starmer."