You can use below tools for deploying docker apps to kubernetes

1. Jenkins with kubernetes CD plugin https://github.com/jenkinsci/kubernetes-cd-plugin

2. Spinnaker

I can share how we are doing it in our start-up.

We've built our own pipeline around Jenkins and Google Kubernetes Engine. There are not that many steps involved:

1. Create a tag of your built image(s): docker tag <source_image> <target_image>
2. Push image(s) to the Google Container Registry: gcloud docker -- push <target_image>
3. Change yaml file definitions to select new <target_image>
4. Update K8s configuration: kubectl apply -f <yaml_file>

Of course in real life this is a little more complex and automatically updates tons of microservices but you get the gist.

Because you asked for tools, there are lots of solutions out there to help you, please have a look at this list to get an overview. It all pretty much depends what kind of environment you want to use it in. Some prominent examples are:

• Werker
• Codefresh
• Spinnaker
• KubeCI