A Trinidad and Tobago Express report said Carew submitted a letter to the regional body on Monday, relinquishing the post he had occupied, on and off, for the last 20 years.
Carew's decision seemed a natural outcome of a public disagreement with Lara over the choice of the Test team against India, which the hosts lost 0-1.
Lara lambasted the selectors and the West Indies Cricket Board and the point of contentions included the captain's role a selector and the alleged biasness of Caribbean pitches towards the Indian bowlers.
Carew, however, refused that these factors prompted his to quit the job and said, ''Those things had nothing to do with it. I advised the Board that I had re-considered my position and decided to let someone else have an opportunity...have a go at it.
I'm just passing the baton on, letting someone else have a say in the future of West Indies cricket.'' Meanwhile, the WICB is expected to choose selectors from among former pace great Andy Roberts, off-spinner of the yesteryears Derrick Parry and Sebastien Lockhart, the 50-year old former Windward Islands opener.
Among the current selectors, former opener Gordon Greenidge and spinner Clyde Butts are expected to be reinstated.
Despite his rift with Lara, Carew felt the ODI team was a good unit but the Test squad has lot of catch up work to do.
''The ODI team is a solid team and is capable of competing with the best teams in the world.
''But we still have a lot of work to do when it comes to the Test squad. And now that will be the challenge of the people who come in as selectors. I wish them all the best,'' he said.
Carew, however, made himself available for any other job and thanked the Trinidad and Tobago Cricket Board for ''the trust they have placed in me, by putting me up as a candidate for the position over the years.''