Mr Tugendhat, who was knocked out in the third round of balloting by MPs, praised Ms Truss's tax-cutting promises and her experience in foreign affairs - drawing two contrasts with rival candidate Rishi Sunak.
"Liz’s plan for the economy is founded on true Conservative principles of low tax, a lean state and bold supply-side reform," Mr Tugendhat wrote in The Times.
"Liz has always stood up for British values at home, and abroad. With her at the helm, I have no doubt that we will move with determination to make this country safer and more secure."
A backbench MP and former soldier, Mr Tugendhat positioned himself the candidate for "a clean start" since he had never served in departing Prime Minister Boris Johnson's scandal-tainted government.
He made it to the final five out of 11 candidates who entered the race, giving him a platform in a pair of TV debates in which he singled himself out by calling Mr Johnson dishonest.
But he was eliminated after coming last in the third round with only 31 votes from MPs.
Although Ms Truss was a closer Johnson ally, Mr Sunak was fined in one of the departing government's ethics scandals, and Mr Tugendhat had struggled to answer whether he could serve under a Sunak government in light of that.
He wrote in his article that Ms Truss could unite the Conservative Party and was the only one of the two remaining candidates who has "convinced me she's ready".
"It is not right that we have the highest tax burden in 70 years at a time of sluggish growth and rising energy prices," he wrote, in an implied criticism of Mr Sunak's record as chancellor.
Mr Tugendhat's backing adds to the growing momentum behind Ms Truss after several polls showed her on course to defeat Mr Sunak in the vote among 200,000 Conservative members.
It follows endorsements for Ms Truss in recent days from Defence Secretary Ben Wallace, a popular figure in the party, and Jake Berry, a prominent voice among Conservatives in the north of England.
Party members will start receiving ballot papers next week. Whoever wins will take over as prime minister in early September, with the next general election expected in 2024.
Put under pressure by Ms Truss's tax-cutting promises, Mr Sunak announced this week he would scrap VAT on domestic fuel bills for the next year to help people through a difficult winter.
Accused of performing a U-turn, Mr Sunak argued that he was offering temporary relief and not the "permanent unfunded tax cuts" he has previously criticised.
In another tack to the right, Mr Sunak was expected to use an appearance in the south of England on Saturday to promise to "safeguard our shared cultural, historical and philosophical heritage" from what he calls "left-wing agitators".
This would involve updating equality guidelines to prevent "mission creep" beyond their original intent, and protecting the expression of unfashionable social attitudes, his campaign said.
Ms Truss meanwhile published an article for My Countryside magazine outlining her pitch to rural voters, which includes abolishing housing targets she has compared to the Soviet Union.
She said her "defining mission" would be to boost Britain's economic growth by cutting and simplifying taxes, reducing regulations and increasing domestic food production.