He called the release "a positive moment for our country's relationship with Pakistan".
Pakistan's army has recovered five Western hostages held by the Taliban for years.
President Trump praised Pakistan for their cooperation and saw Coleman and Boyle's release as a "positive movement" in the relationship between the USA and Pakistan.
"Things here are going about as can be expected", Boyle says in the January video.
The official said the family is free, but Boyle didn't want to board a US transport plane. But this is a country that did not respect us. The marriage ended and the inmate was later released to Canada.
The rescue operation was based on a tip by the US government.
A Canadian couple, who were kidnapped in 2012 during backpacking through Central Asia, have been released after five years, media reports said.
In the video, Joshua Boyle light-heartedly cracked jokes about letters received in reply from their parents in record time and said the conditions of their captivity had improved around the beginning of the year.
In recent days, senior USA officials have been more pointed about Islamabad's alleged ties to militant groups, who are battling against U.S. and American-backed forces in neighboring Afghanistan. The war is at a stalemate.
According to Reuters, the four-nation Quadrilateral Coordination Group (QGC), comprising Afghanistan, China, Pakistan and the United States, has been trying to ease the path to direct talks between the Afghan government and the Taliban, with little success.
"The operation by Pakistani forces, based on actionable intelligence from United States authorities was successful; all hostages were recovered safe and sound and are being repatriated to the country of their origin", the statement said.
USA officials did not immediately confirm a military-style rescue and used far more nuanced language. Canadian officials have said his kidnapping was likely unrelated to his ex-wife's family ties, and friends have said Boyle was a pacifist, raised Mennonite, who became involved with the Khadr family because of his interest in human rights issues.
"I kind of wish he would have told me, because I would have said, 'Hey, dummy, what are you doing?"
"I applaud the innumerable lines of effort from across the U.S. Government", Secretary of State Rex Tillerson said in a statement.
USA officials say Pakistan secured their release. The Haqqanis also have close ties to Pakistan's Inter-Services Intelligence Directorate. "These efforts reflect the best of what America can accomplish".
The Canadian-born Omar Khadr was 15 when he was captured by U.S. troops following a firefight at a suspected al-Qaida compound in Afghanistan that resulted in the death of an American special forces medic, U.S. Army Sgt. Alternately, or perhaps even in parallel, the Pakistanis could have arranged the "rescue" to relieve the Haqqanis of their hostages while protecting the terrorists against an American commando force that might have otherwise been deployed, and regaining millions in foreign aid in the process. "We stand ready to support them as they begin their healing journey", he added. Coleman was pregnant at the time and the couple have had three children while in captivity.