Inter Milan announce the departures of Skriniar, D'Ambrosio and Gagliardini
The 28-year-old Skriniar, who captains Slovakia, has won a Scudetto, two Italian Cups and two Italian Super Cups during six seasons with the Nerazzurri, for whom he made 246 appearances and scored 11 goals.
Skriniar's last season was plagued by injuries as he missed over 20 games in all competitions with Inter, who finished third in the Italian top flight. Skriniar has been linked to a move to Ligue 1 champions Paris St Germain.
"At Inter since the summer of 2017, Skriniar has been one of the protagonists of Inter's extraordinary growth path, which began with their return to the Champions League in 2018...," Inter said in a statement.
D'Ambrosio, 34, will also leave the three-time European champions after almost a decade, having won a Serie A title, the Coppa Italia twice and the Supercoppa Italiana on two occasions.
"284 appearances in the Nerazzurri shirt and almost ten years full of heart, discipline and commitment to the Inter cause," the club said.
"D'Ambrosio arrived in Milano in January 2014... Consistency, determination, versatility and experience have made him a key figure over the past decade, during which he's gained a special place in the fans' hearts..."
D'Ambrosio ends his playing career with Inter after netting 21 times and providing 20 assists.
D'Ambrosio's Italian compatriot Gagliardini will depart the club after joining from Atalanta in 2017 and playing 190 games, in which he scored 16 goals.
The 29-year-old Gagliardini has won a Scudetto, two Supercoppa Italiana titles and two Coppa Italia titles during his time at Inter.
Inter lost to Manchester City in the Champions League last month.