The release and swap of nearly 900 detainees by the two sides in Yemen's conflict began on Friday, the International Committee of the Red Cross said.
The ICRC, which is managing the process, said its planes would be used to carry the released detainees between six cities in Yemen and Saudi Arabia.
Warring parties agreed at negotiations in Switzerland last month to free 887 detainees and to meet again in May to discuss further releases.
Negotiators had hoped for an "all for all" deal involving all remaining detainees during the 10 days of talks held near the Swiss capital Bern. The talks were the latest in a series of meetings that led to releases of prisoners in 2022 and 2020 under a UN-mediated deal known as the Stockholm Agreement.
"With this act of goodwill, hundreds of families torn apart by conflict are being reunited ... Our deep desire is that these releases provide momentum for a broader political solution," said Fabrizio Carboni, the ICRC's regional director for the Near and Middle East.
Riyadh and Tehran last month agreed to restore diplomatic ties severed in 2016, raising hopes that Yemen's peace process would see progress.
A Saudi delegation on Thursday concluded peace talks in Sanaa with the Iran-backed Houthi militias whose officials cited progress and said further discussions were needed to iron out remaining differences.