The defence role will be Shapps' fifth government job in the past year after serving in four different ministries - transport, interior affairs, business and then energy and net zero.
His appointment is unlikely to change Britain's support for Ukraine against Russia.
Shapps replaces Ben Wallace, who said he wanted to step down after four years in the role and would quit as an MP at the next national election.
Wallace confirmed his resignation in a letter to Rishi Sunak on Thursday, offering the government his continued support while warning the British prime minister not to see defence as a "discretionary spend".
Wallace, who helped lead Britain's response to Russia's invasion of Ukraine, was seen as a strong advocate for increased spending on the armed forces.
He had hoped to be a potential successor to NATO Secretary General Jens Stoltenberg but the former Norwegian prime minister's contract was extended by another year.
The departure of the popular Wallace saddened some in the governing Conservative Party.
In his official resignation letter, Wallace renewed his appeal for the government not to turn to defence to make spending cuts.
"The Ministry of Defence is back on the path to being once again world-class with world-class people," he wrote.
"I know you agree with me that we must not return to the days where defence was viewed as a discretionary spend by government and savings were achieved by hollowing out."
He posted on X, formerly known as Twitter: "That's all folks. Been a privilege to serve this great nation."
Sunak praised Wallace for his work, saying in a letter in response: "You have served our country in three of the most demanding posts in government: defence secretary, security minister and Northern Ireland minister."
"I fully understand your desire to step down after eight years of exacting ministerial duties," Sunak said.
A former captain in the British army, Wallace, 53, was appointed as defence minister in 2019 by his friend and ally, former prime minister Boris Johnson after holding junior ministerial roles in earlier governments.
Wallace, alongside Johnson, soon became an ardent supporter of Ukraine after Russia launched its full-scale invasion last year, cajoling other nations to help supply the requests for weapons from Ukrainian President Volodymyr Zelenskiy.
But his frustration with not getting the NATO general secretary post earlier this year bubbled over at the military alliance's summit last month, when he said Ukraine needed to show gratitude and not treat its allies like "Amazon".
He later said in Ukrainian on Twitter that his comments "were somewhat misrepresented" and he instead wanted to emphasise London's relationship with Kyiv was not transactional but more of a partnership.
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