The test will start on Tuesday and is expected to last between six and 48 hours, according to BP executive Kent Wells.
If pressure testing of the well's integrity is successful, it will be kept "shut in" and the leak stopped.
Meanwhile, the Obama administration has sent BP and other parties a fourth bill for response and cleanup efforts.
The administration says the newest bill is for $99.7m (£65.8m).
The oil giant has already fully paid the last three bills totalling $122.2m (£80.6m) for costs related to response and cleanup of the spill, according to the Obama administration.
The test in the Gulf of Mexico will determine if BP's new cap can contain the oil.
This latest move to stop the oil comes the day after the new cap was placed on the leaking well.
Work on the permanent relief well solution continues.
Mr Wells says no promises can be made about whether the new cap will work.
It's not simple stuff. What we don't want to do is speculate around it," he said.
Shutting in the well provides a temporary solution to the leaking oil. BP is continuing work on the relief well that is expected to permanently stop the oil.
If the test goes as planned, it will mark the first time since the explosion aboard the Deepwater Horizon drilling rig on 20 April that the leaking oil has been stopped.
During the tests, BP will be monitoring the pressure of the oil in the well.
High pressure will mean the oil has been contained inside the wellhead.
But if tests show there is low pressure, Mr Wells said this may indicate oil is leaking elsewhere in the well.
He added that if pressure is low the cap won't be kept shut and ships on the surface of the Gulf, like the Q4000 and the Helix Producer, will continue collecting oil.