By following the below steps you can easily transfer your VPS from one Web hosting provider to another and you will not face a single minute downtime:-
1) Before canceling your old web hosting account or server you should order a hosting package with a new hosting provider.
2) Once your new hosting account is the setup you will need to download your entire old web site through FTP program or a cPanel backup utility on your local machine. Then upload your whole website data to your new web hosting account by FTP or using cPanel backup utility again. If you are using FTP, then you will need to re-chmod your folders if you are running scripts.
3) You will need to change DNS(Domain Name Servers) after you have moved all your data to your new hosting account. Before updating the Name servers confirm that everything is working fine by using a temporary address to your new hosting account. Once it is confirmed contact your domain registrar and ask them to update the Name servers and give them DNS given with the login details of your hosting account.
4) Now within 24-48 hours your domain will be fully propagated and be pointing to your new web hosting account.
5) And once your domain is propagated you can cancel your old web hosting account and your website should be fully up and running on your new hosting account.
That’s it, Now you are ready to use your website with your new hosting provider.