The move is reported to be worth an initial £16m, with a further £3m available in add-ons, according to the East Anglian Daily Times, and sees the 26-year-old join newly promoted Ipswich after beating fellow Premier League new boys Hull City to his signature.
Florentino made 31 Premier League appearances for Burnley last season as the Lancashire club were relegated, having initially arrived on loan from Benfica before his move was made permanent this summer. He also has top-level experience in Spain with Getafe and in France with Monaco, spent on loan from Benfica earlier in his career, and has represented Portugal up to under-21 level. His transfer to Portman Road remains subject to his visa application being approved.
"It feels brilliant to be a part of this club," Florentino said.
"I think I will be very happy here. I like how the club sees the future and there are a lot of good players here. How the club is thinking to the long-term is one of the main reasons I came here.
"I can bring experience and balance to the team, between defence and attack, and I like to bring the connection. Now I have signed I can't wait to meet my teammates and the fans and get started with the team."
Ipswich manager Gary O'Neil said: "We are delighted to have added Florentino to the group. He is a player who brings experience of playing in the Premier League as well as other major competitions in Europe, including the Champions League, and makes us stronger in central midfield. He brings quality off the ball, as well as on it, and we look forward to him joining up with the squad."
Born in Angola, Florentino came through Benfica's academy and made his senior debut for the Portuguese giants in February 2019, scoring his first goal a month later as the club won a 37th top-flight title.
Loan spells at Monaco and Getafe followed before he returned to Benfica in 2022 and established himself as a regular in midfield, winning a further league title in 2022-23 and a domestic cup in 2024-25 while gaining regular Champions League experience for the first time in his career.
His season-long loan at Burnley then gave him his first taste of English football, a move that became permanent this summer before his switch to Ipswich was finalised on Tuesday, becoming the club's seventh signing of the window.