Gauke, who was justice secretary himself when Theresa May was prime minister, will report his findings next spring.
The sentencing review comes in the wake of the crisis which saw the government release thousands of prisoners early to free up space in England’s jails.
Gauke, who was one of 21 Tory MPs stripped of the party whip by Boris Johnson after rebelling over Brexit, said: “Clearly, our prisons are not working.
“The prison population is increasing by around 4,500 every year, and nearly 90% of those sentenced to custody are reoffenders.
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“This review will explore what punishment and rehabilitation should look like in the 21st century, and how we can move our justice system out of crisis and towards a long-term, sustainable future.”
Gauke, who stood as an independent at the 2019 election but lost his seat to the Conservatives, has previously said that prison sentences of less than six months should be scrapped.
The review will look at “tough alternatives to custody” while also ensuring the worst offenders continue to be locked up, the Ministry of Justice said.
Mahmood said the review “will ensure we never again have more prisoners than prison spaces”.
She said: “I believe in punishment. I believe in prison, but I also believe that we must increase the range of punishments we use. And that those prisoners who earn the right to turn their lives around should be encouraged to do so.
“The sentencing review will make sure prison and punishment work – and that there is always a cell waiting for dangerous offenders.”
Labour today said the bitter Tory leadership race was providing them with a “wealth of material” ahead of the next election.
Shabana Mahmood, Labour’s national campaign coordinator, said they would “fulsomely” take advantage of the Tories “trashing their own record”.
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She described both Rishi Sunak and Liz Truss as “continuity Johnson” and said she was “happy” to face either at the next general election.
The MP for Birmingham Ladywood said she will be able to tell voters on the doorstep to just listen to the Tories criticising their own record.
In an exclusive interview with HuffPost UK, Mahmood said: “They are giving us a wealth of material, we are obviously using some now and we’ll have plans for more later as the contest progresses and as we gear up for the next general election – whenever that might be.
“We would prefer an earlier election because Rishi Sunak and Liz Truss are proving every day that they are just more of the same.
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“Neither has the answers that the country needs to move forward post-pandemic, neither has the answers on the economy.
“They are just brutally exposing – not just each other – but 12 years of Tory government that has led us to this moment.
“As far as we’re concerned bring on an early general election. As soon as this contest is done they should seek a fresh mandate.”
The vicious battle for No.10 has even prompted Tory grandees to warn the Conservatives they risk being called the “nasty party” again and losing the next election.
“I’ll be able to say to people on the doorstep ‘you don’t have to take my word for it anymore folks just listen to them’. The trashing of their own record, I think that you’d expect us to take advantage of that which we will be doing so fulsomely.”
– Shabana Mahmood
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Earlier in the contest Truss and Sunak pulled out of a Sky News debate amid concerns about the damage they were doing to the party’s reputation, forcing the other candidates to follow suit.
But, despite warnings, the unedifying public slanging match has continued between the final candidates and their campaign teams.
Asked if she thought Tory infighting would help Labour win the next election, Mahmood said: “We’re going to be ready for that election whenever it comes.”
However, she said it was on the Labour Party to persuade the public to switch their votes and that they had to show the public they had “changed” and had the answers on the economy and cost of living crisis.
“The Tories are doing an even better job of trashing their own record than we could do or get a hearing on,” she added.
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“They’re taking primetime broadcast slots to tear lumps out of each other.”
Labour Party deputy leader Angela Rayner, leader Keir Starmer and national campaign coordinator Shabana Mahmood.
JUSTIN TALLIS via Getty Images
Mahmood said the “vicious infighting” brought back memories of some of Labour’s rowing in recent years.
But she added: “The public never appreciates it and they never reward it at the polls either.
“The Labour Party learnt that lesson in the hardest of ways in 2019, we don’t propose to go there again.”
Mahmood said just pointing to the Tories would not be enough and they did not take the electorate for fools: “We know we’ve got to win their trust back.”
She said Labour was earning the right to be heard again, adding: “It’s on us to seal the deal with the electorate.”
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All your bills going up and up and up.
Taxes rising to the highest level in 70 years.
The worst economic crisis for a generation.
Not our words.
The words of those running to be the next Tory leader.
Lord Fowler, who served under Margaret Thatcher and is now a crossbench peer, described Monday night’s BBC debate as “a bad night for the Conservatives”.
He told Times Radio the only people who might have been happy with the outcome would have been the Labour Party, adding: “They’ve got enough clips from that programme to last them through to the next election.”
Yesterday culture secretary Nadine Dorries, who is backing Truss, criticised Sunak for wearing a £3,500 suit and £450 Prada shoes.
Dorries said Truss “will be travelling the country wearing her earrings which cost circa £4.50 from Claire’s Accessories”.
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The comments prompted veterans minister Johnny Mercer to warn that the party was putting success at the next election in jeopardy.
“The puerile nature of this leadership contest is embarrassing,” he said. “Time to raise the standards.”
The Labour party is already weaponising quotes, viral clips and images from the Tory leadership debates on their social media accounts.
They include a “Tory leadership bingo” card that cites “shaking the magic money tree” and “Thatcherite cosplay”.
They also created an advert in which they spliced together clips of Tory leadership candidates tearing strips off of each other over their record in government.
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“All your bills, every week, every month, they’re going up and up and up,” Sunak says in one part of the video.
“Under your plans, we are predicted to have a recession,” Truss tells Sunak in another clip.
Labour leader Keir Starmer even quoted leadership candidates at Boris Johnson during their final prime minister’s questions.
He said: “She [Liz Truss] also said the former chancellor’s 15 tax rises are leading the country into recession and [Penny Mordaunt] was even more scathing.
“She said ‘our public services are in a desperate state, we can’t continue with what we’ve been doing because it clearly isn’t working’.
“Has the prime minister told her who’s been running our public services for the last 12 years?”
Sunak claimed there is “nothing Conservative” about Truss’s approach to cutting taxes and pumping up borrowing, arguing it would give the party “absolutely no chance” of winning the next election.
Foreign secretary Truss, in turn, suggested her rival would lead the country into a recession and criticised him for increasing taxes to the “highest rate in 70 years”.
During the debate a spokesman for Truss told The Times that Sunak was not fit for office, adding: “His aggressive mansplaining and shouty private school behaviour is desperate, unbecoming and is a gift to Labour.”
