Gartside added: "Sammy has played an important role in the club's recent history. We wish him and Frank well for the future.
"Our efforts will now be to look for a replacement manager to concentrate on the future."
Former Wigan boss Paul Jewell is the bookmakers' early favourite, with Chris Coleman, who is at Real Sociedad, as well as ex-Bolton assistant and Hull City manager Phil Brown also believed to be in the frame.
Lee became a coach at Bolton in 2005. His managerial role at the club was his first after being involved in the coaching set-up firstly at Liverpool and then with England.
In the past week, Gary Speed has stepped down as Bolton's first-team coach.
Lee stated Speed had been relieved of his duties and the midfielder would be concentrating on his playing role.
But Speed, 38, insisted he chose to resign to regain his form and his place in the first-team after he was dropped for the recent 1-0 defeat to Chelsea.
It seems last week's fall-out with Gary Speed was the final straw for chairman Phil Gartside
5Live football reporter Juliette Ferrington
Bolton have made it through to the group stages of the Uefa Cup and face tough games against Bayern Munich, Red Star Belgrade, Aris Thessaloniki and SC Braga.
"According to Bolton Wanderers he has left the club by mutual consent," said BBC Radio 5 Live football reporter Juliette Ferrington.
"But would Sammy Lee have wanted to leave bearing in mind he kept talking about being a winner and wanting to get Bolton out of the position they were in?
"It seems last week's fall-out with Gary Speed was the final straw for Phil Gartside.
"This after he left both Speed and club captain Kevin Nolan out of the squad for the game against Chelsea - telling them they were dropped less than an hour and a half before kick-off.
"With Bolton's position in the table, Gartside has decided enough is enough."
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