The 36-year-old departs as one of the most decorated players to have worn Everton's shirt in the club's modern history, despite never lifting a major trophy on Merseyside itself.
His medal haul instead came during a three-year spell at Paris Saint-Germain between his two Everton stints, where he won two Ligue 1 titles and reached the 2020 Champions League final, and with Senegal, whom he helped to Africa Cup of Nations glory in 2021 having earned more than 90 international caps.
Across 236 appearances in blue, spanning his original move from Aston Villa in 2016 and his return in 2022, Gueye built a reputation as one of the Premier League's most relentless ball-winners, twice sharing or winning Everton's Players' Player of the Season prize and taking the club's main Player of the Season honour last term.
Manager David Moyes paid tribute to his influence both on the pitch and in the dressing room.
"Everyone at Everton is hugely grateful for Gana's dedication, professionalism and influence on the pitch throughout his two spells at the club," Moyes said. "His leadership qualities in and around the dressing room proved crucial, particularly in our final season at Goodison.
"His commitment to the club over many years was exceptional. Everyone connected to Everton thanks Gana – he will always be welcome at the club – and we wish him and his family all the very best for the future."
Elsewhere, 18-year-old Akarakiri completed a move to Cagliari earlier this summer after turning down a new contract offer from Everton, ending his spell at the club having progressed through the Arsenal academy before joining Everton in 2024. He made 33 appearances for Everton's Under-18s and Under-21s last season, and his agent, Samuele Mura, explained the thinking behind the move to Italy.
"He made a name for himself at Everton last year; despite being an Under-18 player, he featured for and made his mark in the Under-21s, and this has attracted the interest of many clubs," Mura said.
"The Premier League is a highly coveted league; traditionally, the movement was the other way round. Today, however, there are many English players who are drawn to the Italian league. The decision to bring him to Cagliari stems from the desire to see Demi ready for Serie A and the first team.
"His attributes are particularly well-suited to the Premier League, but there are few players like him in Serie A. Seeking to capitalise on these attributes in Serie A is a key objective in continuing his development."
Mura added that the club had wanted to keep the midfielder.
"He was supposed to stay at Everton, who had offered him a professional contract. We'd been in talks with him for four or five months. Having worked with Italian clubs and seen their interest, we acted immediately to seize this opportunity, given the deadlock with the English club."