Clubs relegated from the Premier League will receive £48million in parachute payments over four years after Football League chairmen voted in favour of the proposal.
The new payments - which rise from £16million a year over two years - will start from next season and are part of a package of solidarity payments from the Premier League to the Football League.
A Football League spokesman said: "Following a frank but constructive meeting at Walsall's Banks's Stadium earlier on Monday, Football League clubs have voted to accept the Premier League's revised solidarity and parachute payments proposals."
The League One and Two clubs had initially blocked the change at a meeting 10 days ago but were told by the Premier League it was a take-it-or-leave-it offer.
The spokesman admitted that many clubs had expressed fears about the changes. Many smaller clubs fear increased money going to the Championship will widen the gap with League One and Two.
The spokesman added: "Whilst many clubs expressed concerns about the proposals, their acceptance was considered the only viable way forward.
"The Football League will now work in good faith, with the Premier League, to ensure that the resulting contract and regulatory changes are good for both competitions and football as a whole."
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