The United States, China and India had been pushing for a rise in production to avert a supply shortage later in the year.
Iran had bulked at the request because it faces sanctions after President Donald Trump ripped up an international nuclear agreement. Mr Trump has also increased pressure on OPEC to raise production ahead of mid-term elections.
Bijan Namdar Zanganeh, Iran’s oil minister, stormed out of the meeting on Thursday evening.
But on Friday, Saudi Arabia’s energy minister Khalid al-Falih had persuaded Mr Zanganeh to accept the proposal Riyadh and non-OPEC member Russia had been championing.
“It will be 1m collectively,” Mr Falih said as he left the meeting, although the final communique did not mention the figure.
The final production hike is expected to less than the 1 million barrels as many producers may struggle to increase production.
The Organization of the Petroleum Exporting Countries met in Vienna in an effort to cool the market after oil prices rose to $80 a barrel.
There is concern among consuming nations and some OPEC members that a shortage and rising oil prices could cripple the global economy.
OPEC and Russia agreed last year to cut production by 1.8 million barrels a day to lift oil prices that had fallen to a low of $27 in 2016.
But production problems in Venezuela and Libya have seen about 2.8 million barrels removed from daily global supply.
Brent oil prices rose 1% to 74.03 in London trading on Friday.