The 50-year-old Dane signed for the club in August last year and proceeded to oversee their greatest ever season, winning the Qatars Stars League (QSL) for the fourth time in five seasons in April before winning the Qatar Cup a month later.
"It was an honour for me," the former Barcelona and Real Madrid star was quoted as saying on the club's website.
"Reaching the quarter-finals of the AFC Champions League was a special end to the season and I thank the players for their responsibility and their ability to overcome difficulties.
"I thank everyone in Lekhwiya club after the cooperation I found and I urge everyone in the club to continue their hard work which made them one of the strongest teams in Asia.
"I am sure this team has a bright future."
Former Lekwiya boss Djamel Belmadi – who oversaw their QSL titles in 2010 and 2011 – will take over from Laudrup.
The Algerian's first match in charge will be against Al Hilal of Saudi Arabia in the AFC Champions League last eight on August 25.