Last month in the Swiss town of Montreux, Yemen's Houthi rebels and the Saudi-backed Yemeni government agreed to exchange 1,081 prisoners, including 15 Saudis.
Three planes took off from the capital of Sanaa today, carrying coalition fighters.
At the same time, an ICRC plane took off from Sanaa airport carrying 76 prisoners to Aden, the ICRC spokesperson said.
"This operation that means so much to so many families is underway", Fabrizio Carboni, ICRC regional director for the Middle East, told Reuters.
The swap was being coordinated by the International Committee of the Red Cross in Yemen.
"It may well be the largest such operation of this kind in the history of prisoner release", he said, adding that his team will soon convene the warring parties to discuss further releases in line with commitments made in Stockholm. The other two planes were Yemenis, and are being flown to Hadramout region, to an area controlled by pro-Saudi government.
One of the aeroplanes was carrying Saudi and Sudanese detainees and flew to Saudi Arabia.
In recent days, Iranian-backed Shiite militiamen have also released two USA prisoners, long in their hands; at the same time, around 200 Houthis were able to return from Oman, where they had gone in the past to receive medical treatment. The Yemeni government and Houthi militia on Thursday began a long-awaited large swap of prisoners as a major breakthrough in peace efforts.
A coalition statement, which confirmed that the plane carrying 15 Saudis and four Sudanese had landed in an airbase in Riyadh, stressed the "political and military leaderships' keenness for the return of all POWs and detainees".
An official reception ceremony was held for the released prisoners upon their arrival at Sana'a airport.
The exchange of prisoners was not officially called a swap as US National Security Advisor Robert O'Brien stopped short of calling it a swap. Saudi Arabian officials tentatively backed the deal, which is unsafe as it permits dozens of Houthi militants to return to the battle zone after receiving training on advanced drones and missiles.
Saudi Arabia and its allies intervened in the country's civil war in March 2015, and have since carried out more than 20,000 airstrikes in an effort to roll back the rebels, with one-third striking non-military sites, including schools, factories and hospitals, according to the Yemen Data Project.
In addition, O'Brien said that the remains of United States citizen Bilal Fateen would also be repatriated.
Yemen has endured years of chaos since the Houthis seized the capital, Sanaa, in late 2014 and ousted former president Abd-Rabbu Mansour Hadi from power.