"We hope to see this type of cooperation and teamwork in helping secure the release of remaining hostages and in our future joint counterterrorism operations", said Donald Trump, in a statement released by White House.
Coleman gave birth to three children in captivity, and Boyle delivered at least one with a flashlight in his mouth before captors brought them "all [their] postpartum needs".
The couple was supposed to return to the U.S.so that Coleman, then pregnant, could deliver her baby.
"So we're waiting for that", his mother, Linda Boyle, said in a video posted on the Toronto Star newspaper's website.
Boyle's sister, Kaeryn, told Xinhua that "We're really glad that they're free".
A U.S. military official said American forces were not involved in any rescue, but that a medical team had been able to meet the family and stood ready to fly them home if needed.
He said there had been a shootout and the last words he heard from the kidnappers were "kill the hostages".
The rescue came as Pakistan and the United States, uneasy allies in fighting Taliban and other militant groups in the region, are experiencing one of the worst lows in relations.
Nawaz Sharif's daughter, son-in-law get bail in Panama Papers case
On Monday, the NAB declared Sharif's sons, Hussain and Hassan, proclaimed offenders for repeatedly failing to appear before it. Sharif's lawyer Khawaja Harris asked the court to adjourn hearing for 15 days with commitment that Sharif would also appear.
They did not say where the family was headed.
The Pakistani army said its forces were able to recover the hostages after acting on USA intelligence about their passage into Pakistan from Afghanistan.
Declining to discuss US intelligence in detail that was shared with Pakistan, they said the United States had been tracking cars capable of holding six or more people moving from place to place, which analysts had concluded were suggestive of moving hostages.
"It was a matter of interdicting vehicles", another USA official told Reuters, saying the United States never dictated to Pakistan how precisely to secure the hostages' release.
It was not clear when the video was shot, but it was released after rumours swirled in Kabul that the government was planning to execute Anas Haqqani, son of the Taliban-allied Haqqani network's founder, who has been held since 2014.
Canadian Foreign Minister Chrystia Freeland asked for respect for the family's privacy. It was revealed Thursday that Coleman had a third child.
Coleman's parents have said they last heard from their son-in-law in October 2012 from an internet cafe in what Boyle described as an "unsafe" part of Afghanistan.
Agents from Pakistan's Inter Services Intelligence (ISI) spy-agency and army soldiers attempted to intercept the vehicle, but it sped away and was chased into a district in northwest Pakistan, according to the security source.