The new regulator would have sweeping powers to sanction clubs who break financial and other rules, and was among 10 recommendations made by MP and former sports minister Crouch in her fan-led review in November.
A new owners' test will also be introduced, including an "integrity test" to protect clubs from unscrupulous owners, while legislation will give fans more say in the running of the game.
However, the regulator would not be able to redistribute the game's vast riches and there are concerns over the Government's timeline, with Crouch describing the unclear schedule for implementing the changes as "worrying".
Her review came in the wake of a number of high-profile scandals in the men's game, including the aborted breakaway European Super League and collapse of Bury.
"I am exceptionally pleased [the Government] has accepted or supported all the strategic recommendations of the review, including committing to legislation for a statutory independent regulator which will regulate financial resilience as well as ownership of clubs," Crouch said.
"This is an enormous step forward in providing much-needed reform for football."
The Government has not announced a timeline for the changes, but will publish a white paper in the summer setting out the proposals in more detail.
The Premier League is opposed to the introduction of a regulator, and Crouch said supporters "remain nervous that this commitment will be delayed or watered down by the vested and conflicted interests in the game which have resisted the much-needed reform for so long".
In a statement released later on Monday, the top-flight said they would work with the Government but reiterated their belief that a statutory-backed regulator is not necessary.
“The Premier League recognises and accepts the case for reform and for a strengthened regulatory system across football,” the Premier League statement read.
“We welcome the clarity from the Government about their position, and are committed to working with them during this next phase of consultation, although we will continue to maintain that it is not necessary for there to be a statutory-backed regulator.
“Since the publication of the Fan-Led Review, the Premier League and our clubs have been working at pace to understand the full impact of the Review’s recommendations and design and implement policies in response to its objectives; including through reviewing our Owners’ and Directors’ Test.
“We agree that fans are of vital importance to the game and their voices should be better listened to across the League. We will be introducing a number of measures to improve this area and plan to make a detailed announcement before the start of the 2022/23 season.
“We are reassured that the Government acknowledges the success of the Premier League and the importance of delivering change that also protects the League’s position as one of this country’s most successful global exports.
“It is this that creates the extraordinary football we see every week in grounds around the country and has enabled our ongoing commitment to support football at all levels by reinvesting an unprecedented £1.6billion outside of the Premier League over the next three seasons.”
Meanwhile, current sports minister Nigel Huddleston said: “It’s just over a year since the failed European Super League bid but it is clear that radical change is needed to protect the future of our national game.
“We will work at pace to establish a strong, independent regulator. However the football authorities can take action now to tackle issues currently facing the game such as the issue of fair distribution of finances throughout the football pyramid and giving fans a greater say in the running of their clubs.”
Huddleston also confirmed the Government would undertake an "in-depth" review of the women's game this summer, which will coincide with the European Championship on home soil.