The 32-year-old has signed a two-year contract to join the Dutch champions as they look to fill the void created by Vurnon Anita's move to Newcastle United.
Ajax manager Frank de Boer told the Dutch media he thinks that Poulsen will be a real asset to the squad.
He said: "Christian Poulsen is a very good player with a lot of experience.
"We were looking for a defensive midfielder to replace Anita. The advantage with Christian is that he has played at the highest possible level.
"He is a top sportsman and a real leader, which is very useful in a young squad like ours."
Poulsen has played for leading clubs in across the continent during his career, including time at Liverpool, Seville and Juventus.