Milan, who lost their Italian league title to Juventus in May, are swelling their ranks having let several older players leave including Gennaro Gattuso, Alessandro Nesta, Filippo Inzaghi, Gianluca Zambrotta and Mark van Bommel.
Dutchman Seedorf, who triumphed in the 2003 and 2007 Champions League finals with Milan to notch up four winners' medals, has joined the band of departures but did not reveal where he is going amid reports he will join Brazil's Botafogo.
"I thank everyone, truly everyone. What emotion," the 36-year-old, a bit part player last term, said.
"I will let you know soon about my future. I am taking my time. I have lots of offers," added the man who is giving his Milan number 10 shirt to Swedish striker Zlatan Ibrahimovic.
Massimiliano Allegri's side have drafted in Fiorentina's Riccardo Montolivo and Nancy's Bakaye Traore for next term but with Mathieu Flamini set to be released, another midfielder should arrive before the August kick-off.
Milan also said in a statement that midfielder Sulley Muntari had undergone surgery on knee ligament damage and is expected to be fit in five or six months.
23-year-old centre-back Acerbi began his career at Lombard side Pavia in 2006 before being recruited by Reggina and moving to Chievo last summer.
Constant also spent time at Chievo, on loan at Stadio Marc'Antonio Bentegodi in 2010-11. He made 32 appearances, scoring twice, before movinw to Genoa where he scored once in 21 games.
He has 12 caps for Guinea and two international goals after featuring for the French under-17 squad as a youth.
The Milan side have also not ruled out the possibility of re-signing Liverpool midfielder Aquilani before the transfer window closes.
The Italian midfielder played on loan at Milan last season, where he scored one goal in 23 league appearances for the Rossoneri.
Milan are looking to reinforce their midfield line with Seedorf departing, plus Gennaro Gattuso and Mathieu Flamini out of contract this summer.
"Before August 31, another midfielder will arrive, it could be Aquilani or somebody else," Milan vice-president Adriano Galliani told Gazzetta dello Sport.
"We haven't spoken yet to Aquilani. He is a Liverpool player."
Aquilani's agent Franco Zavaglia revealed he had not received any offers for his client and that the 27-year-old midfielder was set to return to Liverpool.
Aquilani is under contract with the Premier League side until June 2014 but is considered the ideal replacement for Flamini, who will not be offered a new deal at Milan.