The company has said the next step will be running tests to make sure there are no other leaks from the well. Tests and monitoring could last from six hours to two days.
The old cap, removed Saturday, did not have a tight fit and allowed crude to escape.
BP is drilling two relief wells so it can pump mud and cement into the leaking well for a permanent fix.
The new 150,000-pound metal cap was dubbed the "Top Hat 10."
BP Chief Operating Officer Doug Suttles was careful not to inflate expectations Monday, emphasizing that once the cap is attached, it will take days to know whether it can withstand the pressure of the erupting oil and feed it through pipes to surface ships. The combination of the new cap and surface oil-collecting ships make up BP's plan to stop oil from spewing into the Gulf for the first time since April 20.
"Until we have the cap on, securely fitted in place, and know it's operating per the design, we have to recognize this is a complex operation," Suttles said.
Once the cap is firmly in place, the company will begin "shutting in" the well by closing perforated pipe at the top. The company will be looking to see if the pressure rises inside the cap. If it does, that means there are no other leaks, and the cap is stopping oil from leaking into the Gulf.
However, low pressure levels may mean that oil is leaking elsewhere in the well. If that is the case, Suttles said that BP will work to collect the leak with surface ships and drop yet another cap on top of the stack.
Shuttles said the testing of the new cap should last about 48 hours.
"The danger is you could overpresurize the pipe and cause it to explode, causing many leaks along the pipe," said Dr. Michio Kaku, author of "Physics of the Impossible."
Even if the tests show the cap is successfully holding in the oil, it will not be the final fix for the blown well. That will have to wait until one of two relief wells reaches the leaking well from underground and can inject heavy drilling mud and cement to form a permanent plug.
BP expects one well will do the job, but it's still drilling a second well as a backup. Officials offered mid-August as the most common deadline for when the drilling will be finished.
First lady Michelle Obama travelled to the area to hurt the badly-hurt tourism industry.
"There are so many wonderful places all across the coast..that are ready to welcome visitors like they have every summer," Obama said. "
- A senior adviser to President Barack Obama says the administration is confident that BP's latest effort to contain the oil spill in the Gulf of Mexico will work. At the same time, Obama adviser David Axelrod acknowledges that BP's engineers are in "uncharted waters" when it comes to dealing with the leak.
- Ken Feinberg, the man in charge of administering the $20 billion compensation fund established by BP for victims of the Gulf oil spill, said Saturday he's ready to give those eligible a full six months' worth of emergency payments on a single request. Feinberg also said that speeding up the claims process is part of the effort to help people feel an added degree of financial certainty.
- BP declined to comment on a report that it is talking about possibly selling $12 billion worth of assets, including a stake in Alaska's Prudhoe Bay oil field to Houston-based Apache Corp. The Sunday Times of London newspaper did not cite a source for its report. BP is thought to be considering some asset sales to raise cash to cover its oil spill liability.
The Associated Press contributed to this report.