Accies revealed they had been in talks with the pair about new deals but that both had decided to return to their homelands.
D'Acol, 30, had joined Hamilton two years ago after leaving AEK Athens and played 35 times this season.
Skondras, 27, made 18 appearances after arriving from PAOK in January.
Meanwhile, 20-year-old Jack Breslin has left the Scottish Premiership club to join Clyde.
Breslin, who made his only senior appearances for Hamilton in July, has signed a one-year contract with the League Two club along with 21-year-old fellow defender Jordan Stewart, who was previously with St Mirren.
The news came as midfielder JP McGovern and striker Peter MacDonald, who had ended the season as joint interim managers, left Clyde following the arrival of Jim Chapman from Annan Athletic as team boss.
Brazil-born forward Alex D'Acol and Greek defender Ioannis Skondras have decided against staying with Hamilton Accies at the end of their contracts.