Henman has been without a coach since splitting with Larry Stefanki after the U.S. Open in September.
"Paul and I have been friends for a long time and we got to know each other pretty well when he used to work with Pete (Sampras). I obviously have a lot of respect for him for what they both achieved together," said Henman.
In his own playing career, Annacone reached a career-high singles world ranking of 12. He is better known for his relationship with Sampras, who he coached from 1995-2001
Henman returned to the top 15 in the world last month when he won his first ever Masters Series Event, taking the Paris Masters title with victory over Andrei Pavel.