"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."
Seen as one of the more popular cabinet ministers among Tory members, Wallace was at one time seen as a potential leadership contender.
He ruled himself out of the running for the Conservative leadership last year despite being an early frontrunner in the race to replace Boris Johnson.
The former prime minister praised the outgoing defence secretary and appeared to give his approval to Shapps as a successor.
Posting on Twitter, he said: "Sad to see the departure of my friend Ben Wallace. A fine Defence Secretary who got so many calls right - especially on Ukraine. Grant Shapps is an excellent choice to succeed him.”
Shapps is the first Jewish defence secretary for nearly three decades after Sir Malcolm Rifkind, a Scottish MP whose family emigrated from Lithuania in the 1890s.
He said he was "honoured" to become defence secretary as he praised Wallace's time in the role.
Shapps tweeted: "I'm honoured to be appointed as Defence Secretary by @RishiSunak.
"I'd like to pay tribute to the enormous contribution Ben Wallace has made to UK defence & global security over the last 4 years.
"As I get to work at @DefenceHQ I am looking forward to working with the brave men and women of our Armed Forces who defend our nation's security.
"And continuing the UK's support for Ukraine in their fight against Putin's barbaric invasion."
Shapps, a former BBYO president, told the JC in a 2010 interview, that he was "totally Jewish" saying: "I don't eat pork, we only buy kosher meat and we don't mix meat and milk. I like being Jewish and I married a Jewish girl. It's like a way of life and it's good to be able to instil some of that sense of being in your kids."
