Spain international Thiago, 33, joined Liverpool from Bayern Munich for £20 million ($25 million) in 2020 but injuries have limited the midfielder to just 98 appearances, including only one this season.
"Before he even came to Liverpool I believed that if you really love football it would make a lot of sense if you watched Thiago Alcantara play," said manager Jurgen Klopp, who is also leaving the club at the end of the season.
"Technically, he is so, so good. A talent who could play in any team in the world and it was a privilege to have him with us."
He added: "I know injuries have been a frustration for him and also for us but the level that he was able to play at when he was available was incredible. This is what I will remember."
Central defender Matip, 32, has spent eight years at Liverpool after joining on a free transfer from Schalke, helping the club win a series of trophies including the Champions League and Premier League.
The former Cameroon international, who has made 201 appearances, was one of Klopp's first signings.
Matip has not played since rupturing his anterior cruciate ligament against Fulham in early December.
"In all the years that I have been involved in football, I am not sure I have come across too many players who are more loved than Joel Matip. I'm not even sure it would be possible to say anything bad about him," Klopp said.
"A wonderful professional, a wonderful footballer and a wonderful human being -- we have been blessed to have him with us for as long as we have and now all we can do is wish him well as he heads off in a new direction."
Liverpool host Wolves on Sunday in their final game of the Premier League season, guaranteed to finish third in the table.
