It seems that the missing /home/ubuntu/.aws/config file causes the error message "ERROR: The config profile (eb-cli) could not be found"
I followed instructions in the following gist: https://gist.github.com/RobertoSchneiders/9e0e73e836a80d53a21e, which resolved the issue by explicitly creating this file.
I created ./scripts/deploy.sh file with the following content:
#!/usr/bin/env bash
set -x
set -e
AWS_CONFIG_FILE=$HOME/.aws/config
mkdir $HOME/.aws
touch $AWS_CONFIG_FILE
chmod 600 $AWS_CONFIG_FILE
echo "[profile eb-cli]" > $AWS_CONFIG_FILE
echo "aws_access_key_id=$AWS_ACCESS_KEY_ID" >> $AWS_CONFIG_FILE
echo "aws_secret_access_key=$AWS_SECRET_ACCESS_KEY" >> $AWS_CONFIG_FILE
eb deploy my-environment-production 2>&1 | tee $CIRCLE_ARTIFACTS/eb_deploy_output.txt
# Temporary hack to overcome issue eith 'eb deploy' returning exit code 0 on error
# See http://stackoverflow.com/questions/23771923/elasticbeanstalk-deployment-error-command-hooks-directoryhooksexecutor-py-p
grep -v -c -q -i error $CIRCLE_ARTIFACTS/eb_deploy_output.txt