Here is the AWS CodeBuild buildspec.yml for Jekyll.

aws-codebuild-jekyll-buildspec.yml

# Do not change version. This is the version of aws buildspec, not the version of your buldspec file.
version: 0.2

phases:
  install:
    runtime-versions:
      ruby: latest  
    commands:
      - echo Installing Jekyll...
      - gem install jekyll bundler
      - bundle install
  build:
    commands:
      - echo Build started on `date`
      - echo Generating Jekyll static site
      - bundle exec jekyll build
  post_build:
    commands:
      - echo Build completed on `date`
artifacts:
  files:
    - '**/*'
  base-directory: '_site'