Coach Bob Woolmer described the news as a "huge blow" while captain Inzamam-ul-Haq said Pakistan would now travel to the tournament under "tremendous pressure."
"Akhtar and Asif are both out due to injury and we have decided to replace them with Yasir Arafat and Mohammad Sami," chief selector Wasim Bari said.
"Their injuries will take another two weeks to heal so after consultation with (captain) Inzamam-ul-Haq we have taken the final decision," he added.
"The Pakistan team is capable enough to deal with this critical situation."
Akhtar and Asif had both been having injuries reassessed in England. Akhtar is battling a knee and hamstring injury, while Asif has a recurrence of an elbow injury sustained last year.
There had also been uncertainty over whether they would take a mandatory drugs test ahead of the World Cup.
In November Akhtar was banned for two years and Asif for one year after testing positive for the steroid nandrolone, but the bans were later overturned on the grounds that they took the substance unknowingly.
"It is a huge blow," Woolmer said. "But their injuries would have taken more time and we couldn't wait any more."
"We now know where we stand. It is true that our chances have been hit badly by the absence of these two key bowlers but we will have to show the kind of spirit and team unity which can win us a big event like the World Cup," he added.
The Pakistani team are due to fly out to the Caribbean later Thursday.
"This is not an ideal situation for us. We are leaving for the West Indies under tremendous pressure," Inzamam said.
"But we have shown in the past that through team spirit we can overcome any crisis situation. Mohammad Sami and Arafat may not be as good as Akhtar and Asif but they'll try their level best to make up for the loss."
He added: "We could not take the risk on Shoaib and Asif as the deadline was approaching. We had to take a decision.
"It's up to the available players now to show their mettle so that we can achieve the best possible results in the World Cup."