Lamb worked alongside chairman Steve Gibson as the Teessiders fought back from the brink of financial disaster to enjoy the most successful spell in the club's history, during which they won the Carling Cup in 2004 and reached the UEFA Cup final two seasons later.
He will remain on the Board as a non-executive director as Gibson and new manager Tony Mowbray attempt to steer Boro back into the top flight.
Lamb said: "After almost 25 years in the role during some of the most challenging, exciting and successful periods in the club's history, the time is right for me to make way for someone else.
"I have enjoyed every minute of my time as chief executive and now look forward to exploring new opportunities and challenges.
"I want to thank all the staff who have given me their help and support during my time at the club. I am pleased that with Tony Mowbray and [assistant manager] Mark Venus at the helm, the club is able to look forward to an exciting future."
Source: PA
Source: PA