Wilfried Bony claims to be fully focused on Swansea at the end of a summer in which his future was called into question.
Charlton Athletic manager Bob Peeters has sought to play down rumours linking him with Darren Bent and Danny Graham.
The 32-year-old midfielder was a free agent following his release by French side Evian at the end of last season and has agreed terms on a contract until June 30, 2014 subject to the successful completion of a medical.
Ajax's director of football Marc Overmars welcomed the arrival of the former Liverpool, Juventus, Sevilla, Schalke and Copenhagen player.
"We are very pleased with his choice to come and play with Ajax, for he could have gone to several clubs in Europe," said Overmars.
"He is a leader, both on and off the field, and that can help our young group of players."
Poulsen won 92 caps for Denmark since making his debut in November 2001, but called time on his international career earlier this month.