The 23-year-old Dane raced for the team during their 2014 campaign, securing a podium on debut in Australia, but lost his seat as Fernando Alonso was recruited for 2015. He has served as reserve driver this year, but with newly-crowned GP2 champion Stoffel Vandoorne also on McLaren's books, the team confirmed they can no longer offer a role to Magnussen.
"Kevin has always done a very impressive and professional job for McLaren in the five years since he joined our Young Driver Programme in 2010," said Ron Dennis, Chairman & Chief Executive Officer of McLaren Technology Group.
"In 2014 he raced very well alongside Jenson, who is a hugely experienced and very quick world champion. Kevin's Grand Prix debut in Melbourne last year was rewarded with a podium that day that he, and we, can be justifiably proud of.
"Kevin has continued to work hard for us in 2015, supporting Fernando and Jenson, although he was understandably frustrated not to be racing.
"He is extremely keen to return to racing next year, and, in keeping with our tradition with our young drivers, we will not stand in the way of his ability to fulfil his ambition and potential.
"Evidently, we have no space for him at McLaren-Honda as a race driver next year, but there is no shame in being edged out by two world champions, Fernando and Jenson. We wish Kevin well, and will do all we can to help him successfully embark on the next chapter of his racing career. He is a very talented racing driver, and he deserves to have a Formula One career."
Magnussen, who beat Vandoorne to the 2013 Formula Renault 3.5 crown, insisted he would 'never give up on the dream', stating on social media: "I want to say thank you to my friends at McLaren. There are a lot of great people there. Good luck guys."
Though McLaren's 2016 race seats are now full, a number of teams still have unconfirmed slots for next season, including Lotus, Marussia and the new Haas squad.