Chairman Huw Jenkins says Swansea were disappointed to see Ashley Williams join Everton but had "reluctantly" agreed to his transfer request.
Wales captain Williams, 31, has joined the Toffees for an undisclosed fee, thought to be up to £12m with add-ons.
"It is definitely not something we wanted to happen," Jenkins told the Swans' website.
"But having turned down Everton's initial offer, Ashley expressed his desire for a new challenge."
Jenkins continued: "Taking into account the excellent service Ashley has given this football club over the last eight years, including as club captain, we reluctantly agreed to his request to join Everton after they made an improved offer.