WhAT I HAVE:
Domain mydomain.xxx registered with domain registrar who doesn’t allow change NameServers or DNS management.

Old Host where my domain is already pointed, and its:
IP is 111.111.111.111
1st Name server: ns1.oldhost.com
2nd Name server: ns2.oldhost.com
Also, I have WHM/cPanel with “Edit DNS Zone” function for mydomain.xxx DNS management, see attached image.

New Host where I need redirect my domain, and its:
IP is 222.222.222.222
1st Name server: ns1.newhost.com
2nd Name server: ns2.newhost.com
I have WHM/cPanel with this host as well.

THE PROBLEM I MUST SOLVE:
I need redirect completely mydomain.xxx domain fromOld Host to New Host by “Edit DNS Zone” of WHM/cPanel on Old Host.

I think this is possible easily, but what should I modify in mydomain.xxx “Edit DNS Zone” ?

In that figure, change all instance of IP 111.111.111.111 to new IP 222.222.222.222 to point your domain to new server.

Better change your registrar.

As Vinsar have said, change all of the IPs under the A record to the new provider's server IP and it should work fine. However, do take note that in the future if you need to create a subdomain at the new host, you will also need to create a subdomain at the old host and edit it's A record to point to the new provider's server. :agree:

What about NameServers?
Should I change Old Host's nameservers ns1.oldhost.com and ns2.oldhost.com to New Host's nameservers ns1.newhost.com and ns2.newhost.com?
(field 14 and 19 In the image http://www.webhostingtalk.com/attachment.php?attachmentid=15235&d=1248105007 )

No you should leave them as they are.

..... registered with domain registrar who doesn’t allow change NameServers or DNS management.



will the old host let you continue using their nameservers after you move the website?

will the old host let you continue using their nameservers after you move the website?
I believe what he meant by this is the nameservers shown in the DNS zone within WHM.

will the old host let you continue using their nameservers after you move the website?

Yes, I am continuing using old host as well, I have some websites hosted on my old host. But also I have some new hosts as well.
According past experience to have only one hosting provider is very risky.