Recently I wanted to create a hosted zone on AWS Router53 for my domain from OVH. It's a very simple operation.
Go to AWS Route53, select Hosted zones from the left menu and click on Create Hosted Zone button. In the form on the right, type Domain Name.
Click Create button on the bottom of the site. AWS site should redirect you to list of records. You should see a record with NS type. We have to set those values in OVH domain configuration.
Log in to OVH account, go do domains, select domain and go to DNS servers tab.
Warning. If you want to keep existing zones, create the same zone records in Route53 at first - just copy them from DNS zone tab on OVH.
On the right, click on the Modify DNS servers button. Replace (and add two more) OVH servers with AWS servers from NS type record.
Click Apply configuration button. It's everything. We have to wait because propagating changes takes some time. If you moved zones from OVH to AWS Route53 before changing DNS servers, there shouldn't be any downtime.
OVH blocks DNS update for 24 hours to avoid validation failure on your domain. If you want to speed up the operation, go to Recent tasks tab and use edit icon on the right.
You can remove everything from DNS zone later because it won't be needed.