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.
“It goes without saying that we wish him the very best with his new challenge and thank him for his services.”
Williams, whose contract is due to run until 2018, has played more than 350 games for the Swans since joining for £300,000 from Stockport in March 2008.