Lee is more famous for his time at Liverpool and England and will replace new Derby boss Phil Brown with immediate effect.
The national coach will leave his full time position with the FA but still continue his role as part of Sven Goran Eriksson's coaching staff.
Lee said, "I've really enjoyed my time with the FA. There are so many tremendous people working there who are firmly commited to developing and improving every aspect of the game.
"However, the opportunity Sam Allardyce has offered me with Bolton is too good to ignore. Bolton are a club that have made incredible progress in recent years and it will be great to join them as they kick off their first ever European campaign.
"I'm also delighted that I will be continuing my role with the England team as we continue our qualification matches for next year's World Cup. I'd like to pay tribute to Bolton and The FA for allowing me the honour of maintaining my role with the national team."