The left-handed opener, who retired from international cricket in 2018, played his entire county career with Essex.
"It is not easy to say goodbye. For more than two decades, cricket has been so much more than my job," he said in a statement on the Essex website (www.essexcricket.org.uk).
"It has allowed me to experience places I never dreamed I would go, be part of teams that have achieved things I would never have thought possible and, most importantly, created deep friendships that will last a lifetime."
Scorer of 12,472 test runs for England and capped 161 times, Cook said it was the right time to go and "make way for the new generation to take over".
Cook was England's test captain from 2012 to 2017 and also captain for 69 one-day internationals from 2010 to 14.
He scored 766 runs in seven innings during the 2010-11 Ashes tour to help England to their first series win in Australia for 24 years.
