How to keep Jenkins configurations in a git repository. Put .gitignore in Jenkins’ home directory (/var/lib/jenkins). Initialize a git repository and add a remote to push to. Create a new Jenkins job to run e.g. nightly with the content of backup.sh as shell execution build step.

.gitignore

# Non-config file types
*.log
*.log.*
*.tmp
*.old
*.bak
*.jar
*.jpi
*.jpi.pinned
*.json

# Security related
/.ssh
/secret.key*
/secrets
/credentials.xml
/identity.key
 
# Generated Jenkins state
/.owner
/queue.xml
/fingerprints/
/shelvedProjects/
/updates/
 
# Tools that Jenkins manages
/tools/
/cache/
 
# Extracted plugins
/plugins/*/
 
# Job state
builds/
workspace/
lastStable
lastSuccessful
nextBuildNumber
modules/

# Interactive shell stuff
.bash_history
/.vim*
.lesshst
.Xauthority

# Package cache
/.gradle/caches
/.ivy2/
/.m2/
/.node-gyp/
/.npm/
/.sbt/

# TFS plugin
/.microsoft

# FOP cache
/.fop

# Fontconfig cache
/.cache

backup.sh

# Move into the Jenkins master directory
cd $JENKINS_HOME

# Add all new, changed and deleted files
# Unwanted files must be listed in .gitignore
git add --all

# Commit, and ignore if the commit is empty
git commit -m "Jenkins config change" || true

# Push changes outside of the Jenkins directory
git push

This is great, but what might be more effective is reversing the gitignore to ignore everything by default and only include the config.xml files (and whatever else). Something like:

*
!*config.xml
!jobs
!jobs/*
!jobs/*/config.xml

@thegoldenmule "and whatever else" is the tricky part. Your approach requires knowing when Jenkins adds new config files or changes their locations. OP's approach will find anything new/unrecognized.