The move follows the controversy surrounding Mayo TD Beverley Flynn, who continued to receive the €41,000-a-year independent TD's allowance even after rejoining Fianna Fail.
However, it is unclear how much money -- if any -- the changes proposed by the Oireachtas Commission will save the exchequer.
The new system features a monthly all-in allowance for attendance at votes, debates and committee meetings.
It will involve the introduction of attendance recording and deductions for being absent, while party whips will play a key role in the verification process.
Ceann Comhairle John O'Donoghue said the changes will be "cost neutral".
"This is a significant action. It represents a real break with long-standing tradition and is a clear demonstration of how members of the Oireachtas are not only transparent and accountable, but will now be seen to be to a greater degree," he said.
"I am pleased that my commission colleagues have adopted this progressive and important step," added Mr O'Donoghue, who is chairman of the commission that oversees the budget for the Houses of the Oireachtas.
Fine Gael had proposed the current system of allowances and expenses be scrapped.
Deputy Leo Varadkar (FG) said he was disappointed Mr O'Donoghue decided against a requirement for TDs and senators to submit receipts.
However, he admitted such a system would require additional staff, at extra cost.
Currently, TDs can claim a daily attendance allowance even though their attendance is never checked against the Dail voting record. They are also entitled to a daily travel and subsistence payment.
The commission's recommendations will now be forwarded to the Minister for Finance Brian Lenihan who will make the final decision on the proposal.