Ms Mordaunt, the Minister of State for Trade Policy, made the surprise announcement after narrowly losing to Ms Truss for a place in the final two in the Conservative Party leadership race with Rishi Sunak.
She called the Foreign Secretary the "hope candidate" as she opened the latest hustings in Exeter - the second out of 12 in the Tory race, which came as members start receiving their ballot papers this week.
Ms Truss made her latest pitch to members by saying she would "take on the Whitehall orthodoxy" and tackle what she regards as "left-wing groupthink" by shaking up the civil service.
This would involve cutting civil service time off, reducing pay for people outside London and scrapping the number of diversity officers working for government departments.
Ms Mordaunt's intervention was the latest high-profile endorsement for Ms Truss in recent days following Defence Secretary Ben Wallace, Chancellor Nadhim Zahawi and prominent northern MP Jake Berry.
Ms Mordaunt, the MP for Portsmouth North, said the Conservatives would “short-change the country, we may lose an election” if they made the wrong decision.
“I could have remained undeclared, I could be off sipping pina coladas right now but I’m not because this is too important and I’m not going to leave this to chance,” Ms Mordaunt said.
She said choosing between the two candidates was hard.
“Who can lead?" Ms Mordaunt asked. "Who can build that team and deliver for our country? Who does have that bold economic plan that our nation needs?
“Who has got reach? Who can relate to people? Who understands that people need help with the cost of living now? And who is going to rightly clobber our opponents?
“Who is going to hold seats and win back councils and who most embodies the vision and values the British public had in their heads and their hearts when they voted in 2016 and 2019?
“At the start of this final phase of this contest, I didn’t know the answer to those questions but I’ve seen enough to know who the person I’m going to put my faith in is – and that is Liz Truss.”
Tory members cheered the announcement.
“Her graft, her authenticity, her determination, her ambition for this country, her consistency and sense of duty — she knows what she believes in, and her resolve to stand up against tyranny and fight for freedom," Ms Mordaunt continued.
“That’s what our country stands for and that’s why I know with her we can win.
“And actually seeing her over the last few weeks has made me want to help her, to help her win, to help build the team we need to win the country, and to give ourselves as a party and as a nation the pride and confidence we need to reach our full potential.
“In short, folks, to give us all hope. She for me is the hope candidate.”
Ms Truss, in her opening speech, said of Ms Mordaunt: “She’s a great person, she’s a great politician, she’s a great patriot and I’m proud to call her my friend.”
The unity between the two Conservative MPs was in stark contrast to earlier exchanges in the leadership campaign, which saw allies of Ms Truss deny involvement in a “black ops” campaign against Ms Mordaunt.
The latest event in Exeter involving Ms Truss and Mr Sunak was a calmer affair than the live TV debates, with both candidates appearing separately on stage to face questions.
Ms Truss called the Treasury a hindrance and said changes were needed to the way it operated if she were to become prime minister.
Asked if the Treasury should be broken up, she laughed as she said: “Well, I wouldn’t want to give them any advance warning if I was going to do that.”
“I do think the Treasury needs to change. And it has been a block on progress.”
Former chancellor Mr Sunak criticised the Foreign Secretary’s economic plans.
“I want to reform the corporate tax system," he said to applause.
"Liz Truss’s policies on corporate taxation are exactly the failed Treasury orthodoxy of the last 10 years, which hasn’t worked.
"I want to change it and grow the economy.”
Ms Truss also signalled a departure from her 2014 desire to repeal the Hunting Act 2004, a piece of legislation that led to a ban on fox hunting in England and Wales.
“I remember being a minister under David Cameron’s government and looking at this issue, and I think opening Pandora’s box could possibly make the situation worse for people who enjoy country sports,” she said.
Mr Sunak outlined a greater role for technology in reforming the National Health Service.
“Right now we’ve got this massive problem with the backlogs and, as they’ve already done in some trusts, we can use software automation and AI to massively rip through all of the triaging and processing of them and clear up the lists, and that’s going to clear up processing times,” he said.
But while the tone of the event was largely devoid of attacks by Tories on Tories, Ms Truss criticised “attention seeker” Nicola Sturgeon, the First Minister of Scotland.
“I think the best thing to do with Nicola Sturgeon is ignore her,” she said.