The 26-year-old Spaniard, who was released from his contract two years early, said that he "never really felt at home" with Ron Dennis' team after joining them from Renault, with whom he won the world championship in 2005 and 2006.
"Since I was a boy I had always wanted to drive for McLaren," Alonso said, "but sometimes in life things do not work out.
"I continue to believe McLaren is a great team. Yes, we have had our ups and downs during the season, which has made it extra-challenging for all of us, and it is not a secret that I never really felt at home."
At the crux of his decision to quit was the fact that he was never given preferential treatment over his British team-mate Lewis Hamilton, who he won the same number of races as and finished equal points with in the championship.
Despite speculation that Hamilton had been favoured by team boss Ron Dennis in the title run-in, Alonso said that no such situation had arisen.
"I know there have been suggestions of favouritism within the team and people say a lot of things in the heat of battle," he added.
"But in the end I was always provided with an equal opportunity to win. Today's decision allows all of us to focus on 2008, and I wish the team, Vodafone, Banco Santander, Mutua Madrileña and all the other team partners who I have worked closely with during the year, the best for the future."
Alonso is not believed to have been made to pay McLaren any compensation as part of his release, but is understood to have signed a release agreement preventing him from racing from any of their direct rivals for next season.
Whether or not his former team Renault, whom he drove for between 2003 and 2006, are classed as direct rivals is open to debate, but the team have expressed an interest in taking him back and have two seats available at the moment.
Williams - for whom Alonso's former chief mechanic Rod Nelson now works - and Toyota have also been linked with a bidding war for his services.