The controls agreed in February were ratified and will see increases in players' wage bills limited and clubs only allowed to make maximum losses of £105million over three years.
One concession was agreed however, meaning that any profits from player sales will not be part of the spending restrictions on players' wages.
Former Arsenal vice-chairman David Dein warned however that the league would need to be "vigilant" to ensure clubs were not getting around the rules.
In February, the 20 club chairmen agreed by the narrowest majority to bring in the two main controls with 13 in favour, six against and one abstaining.
The vote, written down rather than a show of hands, was more decisive with 14 clubs in favour, five against and one abstention.
The salary restraints state that clubs with a total wage bill of 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 - and now nor profit from player sales.
Any club breaching the rules will face tough sanctions - and Premier League chief executive Richard Scudamore has said they would be pushing for points deductions.
Of the 20 clubs in the top flight, Manchester City, Chelsea, Aston Villa and Liverpool have reported losses of more than £105million over the last three years, according to the most up-to-date published accounts.
Dein welcomed the agreement but warned: "In my experience clubs will do what they want to do. There's going to have to be a lot of vigilance to make sure people don't try to get around it.
"This should lead to more stability and there should also still be the dream factor with clubs being able to come up through the lower divisions to the Premier League and win the league or the FA Cup."
Two clubs changed their position from February including Swansea, who initially opposed the regulations but who abstained.
Reading abstained in February but voted in favour at the meeting.
The five clubs who voted against were Manchester City, Fulham, West Brom, Aston Villa and Southampton.
FA chairman David Bernstein welcomed the agreement.
He said: "There is stress on clubs that none of us have wanted to see, with all the changes taking place in football.
"So it's good to see that bit by bit UEFA, the Football League and the Premier League are taking a step in the right direction."