Llambias has made the decision after five years at St James' Park, acting as owner Mike Ashley's right-hand man.
Llambias arrived in 2008, taking over from Chris Mort, but he has now decided that the time is right to leave.
"I have had an incredible journey during my five years at the club, including some challenging times," said Llambias.
"I will reflect with great fondness on my time in the North East and, in me, Newcastle United have a lifelong supporter.
"I want to thank the staff for their hard work, our fans for their support of the club, and wish them all well for the future."
Llambias's decision comes just days after Joe Kinnear was appointed as the club's new director of football.
Llambias, who has worked closely with United owner Mike Ashley since he took over the club in 2007, has polarised opinions of the club's fans during his time at St James' Park.
He has overseen the sales of some of the club's most popular players, such as
Andy Carroll and Kevin Nolan, while also being involved in controversial decisions such as the one to appoint Kinnear as manager in 2008 and changing the name of the club's famous ground.
There have been positives too - the club's smart recruitment and wage policy was heralded when they finished fifth in the 2011-12 season, but a troubled last campaign stirred things up once more.
Kinnear's return to the club, which he announced on Sunday but the club did not confirm until yesterday, caused outrage among Newcastle fans, with the 66-year-old giving a radio interview during which he insulted them.
He also pronounced a number of first-team player's names wrong, while also referring to Llambias as Llambeeze.
The ex-Wimbledon manager correctly called Llambias' resignation, before claiming to have replaced him, even though Llambias' job was a different one.
He told talkSPORT: "I only signed the contract last night. So that was someone speaking to Mike but it's been ongoing for the last three weeks.
"Derek Llambeeze was the director of football. Derek has resigned now."
Kinnear would go on to muddle up a number of players before telling dissenting fans he had "more intelligence than them, that's for sure".
When asked what he would say to the fans, he added: "To all the Newcastle fans who don't do this decision then shall I bring Llambeeze back?"
Llambias arrived at Newcastle in the summer of 2008 and was criticised by the supporters for being part of a so-called 'Cockney Mafia', comprising of himself, Ashley, Tony Jimenez and Dennis Wise, who was installed as a director of football.
Between them they signed a number of previously unheard-of players, some of which have proved successful - Fabricio Coloccini and Jonas Guttierez - while others, such as Xisco, failed to impress.
Newcastle have been linked with a move to sign Dutch defender Douglas but Sky Sports understands the club have now decided against signing the Brazilian-born stopper.
Douglas is available on a free transfer after leaving FC Twente, and an agreement with Newcastle was on the cards.
However, the 25-year-old will now not be moving to St James' Park. Sky Sports understands that the decision was made by Kinnear.
It is understood Kinnear has already identified other defensive targets for the club to move for this summer.