The 29-year-old Argentine centre-back, who joined from Feyenoord in 2022 for €15 million, turned down multiple contract offers from the Cherries and has been free to speak to European clubs since 1 January. He has made 126 appearances for the club across four seasons.
"From the first day I arrived, I felt at home at this club. I'm proud of everything we achieved over the last four years and I'm grateful for the support the fans have always given me."
"Bournemouth will always hold a special place for me and I will look back at my time here with fond memories. For now, there are still two big games left of the season and I'm looking forward to seeing what we can achieve together."
Transfer reporter Ben Jacobs confirmed that Tottenham already have an agreement on personal terms with Senesi, contingent on avoiding relegation. The north London side are currently two points above the drop zone with two games remaining.
Manchester United have also registered interest as they look to address the injury vulnerabilities exposed by the absences of Matthijs de Ligt and Lisandro Martínez this season. Liverpool's move is described as contingent on whether Ibrahima Konaté remains at the club. Barcelona, Juventus, Atlético Madrid and Roma have also been linked.
Senesi made only his second and third international appearances for Argentina during this campaign, a sign of a profile that has grown substantially since his arrival on the south coast.
His departure comes as Bournemouth also prepare for life without head coach Andoni Iraola, who announced in April he will leave at the end of the season.