Spurs already had an agreement in place with the 29-year-old defender since March, and now the deal is close to becoming a formality.
According to Fabrizio Romano, Senesi will sign a four-year contract in north London and become their second capture of the summer after agreeing a transfer for Andy Robertson.
Senesi played 37 of Bournemouth's 38 Premier League games this term as the Cherries qualified for the Europa League, but will see joining Tottenham as a new challenge.
A move to Roberto De Zerbi's side will be a welcome piece of good news for the defender, who was recently omitted from Argentina's World Cup squad.