Rehman has been on the U.S. radar for years. In 2010, Washington offered $5 million for information leading to Rehman under their "Rewards for Justice" program.
While Rehman was mostly known for his activities in Pakistan, the U.S. said in its announcement that he also participated in cross-border attacks in Afghanistan against U.S. and NATO personnel.
The U.S. wanted Rehman in connection with his alleged involvement in an attack on a U.S. base in Khost, Afghanistan in 2009. The attack on Camp Chapman killed seven Americans working for the CIA, a Jordanian intelligence officer and wounded six other CIA personnel.
Pakistan's incoming prime minister, Nawaz Sharif, has repeatedly said he is against the use of American drones on Pakistani soil, and Pakistani officials have demanded publicly that the program be stopped.
Sharif has said he would be open to negotiating with the Pakistani Taliban in order to end the fighting in the tribal agencies. Rehman's death could complicate that.
"He was a very cool-minded person, a very intelligent person and he was someone that the government could talk to," said Mansur Mahsud, director of administration and research at the Islamabad-based FATA Research Center.
Rehman was believed to be about 42 or 43 years old and was from South Waziristan, Mahsud said. He had already been fighting American troops in Afghanistan when the TTP was created in late 2007 and he turned his focus onto Pakistani targets.
The Ministry of Foreign Affairs condemned the drone strike Wednesday but made no mention of Rehman in their brief statement.
"The Government of Pakistan has consistently maintained that the drone strikes are counter-productive, entail loss of innocent civilian lives, have human rights and humanitarian implications and violate the principles of national sovereignty, territorial integrity and international law," the ministry said.
Senior civilian and military officials are known to have supported some of the attacks in the past, but many say that is no longer the case.
Pakistan has been hit by 355 such attacks since 2004, according to the New America Foundation, a U.S.-based think tank. The figure does not include Wednesday's strike. Up to 3,336 people have died in the strikes, according to the think tank.
Obama's speech last Thursday was his most extensive comments to date about the secretive drone program, which has come under increased criticism for its lack of accountability.
The president cast drone strikes against Islamic militants as crucial to U.S. counterterrorism efforts but acknowledged that they are not a "cure-all." The president also said he is deeply troubled by civilians unintentionally killed in the strikes and announced more restrictive rules governing the attacks -- measures that his advisers said would effectively limit drone use in the future.
White House spokesman Carney said the new standards do not mean the administration would discuss details of every counterterrorism operation.