The 20 club chairmen voted by 13 to six - with one abstention - to implement two significant controls - to limit players' wage bills from next season, and longer-term measures that will restrict the amount of losses clubs can make to £105million over three years.
Sources say Fulham, West Brom, Manchester City, Aston Villa, Swansea and Southampton all voted against. Chelsea, who had initially been viewed as opponents of financial fair play regulations, voted in favour. Reading abstained.
Clubs whose total wage bill is more than £52million will only be allowed to increase their wages by £4million per season for the next three years, though that cap does not cover extra money coming in from increases in commercial or matchday income.
The effect of the financial controls should prevent hugely wealthy owners achieving the almost-overnight success of Chelsea and Manchester City.
Any club breaching the rules will face tough sanctions - and Premier League chief executive Scudamore said they would be pushing for points deductions.
Scudamore told reporters: "As all things in our rulebook you will subject to a disciplinary commission.
"The clubs understand that if people break the £105m we will looking for the top-end ultimate sanction range - points deduction.
"Normally we stay silent on sanctions as the commission has a free range, but clearly if there is a material breach of that rule we will be asking the commission to consider top-end sanctions."
Of the 20 clubs in the top flight, only Manchester City, Chelsea and Liverpool have reported losses of more than £105million over the last three years, according to the most up-to-date published accounts.
Scudamore said there would be an "absolute prohibition" on clubs reporting losses of more than £105million over the next three years with the first sanctions possible in 2016. He said that the measures would mean it will take longer for benefactor owners to achieve success - but that it would still be possible.
He said: "The balance we have tried to strike is that a new owner can still invest a decent amount of money to improve their club but they are not going to be throwing hundreds and hundreds of millions in a very short period of time.
"While it has worked for a couple of clubs in the last 10 years, and I am not critical of that, if that's going to be done in the future it's going to have to be over a slightly longer term without the huge losses being made.
"I think at £105million you can still build a very decent club with substantial owner funding but you have to do it over time, you can't do it in a season."
Chelsea won the Premier League two years after Roman Abramovich's takeover, and Manchester City's title success came three years after Sheikh Mansour's takeover.
Any club making any loss of over £5million a year will have to guarantee those losses against the owner's assets.
"In some ways that's the most significant part, this is a three-year rolling system of secure funding - it's one year at the moment," Scudamore added.
The ceiling when the wage increase restrictions kick in will be £52million next season, £56million the following year and £60million i 2015/16. Only seven of the current top-flight clubs would be under that ceiling at the moment.
The Premier League's legal advisers will now work on the detailed proposals and these will be brought back before the chairmen in April to be ratified.
In a statement, Chelsea said they are supportive of moves that promote financial stability.
The statement said: "Premier League clubs today reached an agreement to introduce financial stability rules and wage controls for the league. Chelsea Football Club is supportive of moves that promote financial stability in football. We are already subject to UEFA's financial fair play principles and will comply with those.
"The new rules will be subject to further detailed discussions before they are brought in and we will play our part in those to ensure implementation is fair for all clubs in the league."
West Ham's co-owner David Gold said the proposals would prevent Portsmouth's descent in administration happening again.
He said: "It's not a salary cap - it's a restraint on over-spending. If clubs increase their revenues then they can increase their spending.
"We have got restraint - that's the important thing. What's driving the whole thing is we've got to avoid another Portsmouth."