The firm is checking how much pressure the well can withstand while the valves on its new capping device are closed.
US President Barack Obama hailed the move as a "positive sign", and BP's shares rallied in early trading in London after sharp rises in New York.
Oil has been flowing from the well since a rig exploded on 20 April.
Eleven workers were killed in the Deepwater Horizon explosion, and the oil spill has raised fears of an environmental catastrophe.
BP has tried a number of ways to stop the flow, but the new capping device is the first to have succeeded in stopping it entirely.
BP executive Kent Wells announced the success on Thursday, saying he was "excited" by the progress.
The firm will now monitor the integrity of the well in detailed tests expected to last until Saturday, with experts discussing the progress every six hours.
The valves staunching the flow of oil will then be reopened and oil will be again channelled on to containment ships on the surface while experts examine seismic data garnered from the tests.
If the well can withstand the pressure, then the valves can be shut again.

Comments
nobody has commented on this post yet, but I'm sure they will!
(sign in to comment)