Ok, I am assuming by "i want to have wordpress on separate virtual host" you mean you will host it on a separate server ( a virtualhost in this context is an apache configuration to support a different subdomain or domain and it sounds like that's not what you're trying to configure).

For this lets use:

server1.example.org (The site where example.org will be pointed and the server hosting your static web content)

server2.example.org (The server that will host your WordPress blog) - We will assume that WordPress is already up and running here.

example.org (the domain that will be used for both).

You'll want to use a plan Ubuntu droplet for server 1 and you can use the WordPress one-click image for the second if you like.

Point your domain name to server1's IP address in your DNS configuration for this domain.

On server 1, install nginx

sudo apt-get update
sudo apt-get install nginx

Now you can upload your static html site to /usr/share/nginx/html and the site should be viewable by browsing to your droplet's IP address.

Next we will set up a proxy configuration in nginx so that everything for /blog is proxied to your WordPress droplet.

Open the file /etc/nginx/sites-enabled/default and edit it so it looks like this:

server {
    listen 80 default_server;
    listen [::]:80 default_server ipv6only=on;

    root /usr/share/nginx/html;
    index index.html index.htm;

    server_name example.org www.example.org;

    location / {
        try_files $uri $uri/ =404;
    }

    location /blog {
        proxy_pass http://your wordpress droplet's IP/;
        proxy_set_header Host $host;
        proxy_set_header X-Real-IP $remote_addr;
        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
        proxy_set_header X-Forwarded-Proto $scheme;
    }
}

Save these changes and restart nginx with:

sudo service nginx restart

Now you'll want to access your WordPress droplet directly by it's IP address and log into wp-admin. In settings, change the base_url settings to http://example.org/blog

Now you should be able to view your static site at http://example.org and your wordpress blog at http://example.org/blog

Hi @ryanpq ,

Thanks for this answer, it helped me a lot.
I still have a problem though: my website is initially loaded over https, so when I proxy_pass to http://wordpress droplet's IP/ at /blog location , my content (JS + CSS) cannot load.

And if I proxy_pass to https://wordpress droplet's IP/, I get a 502 BAD GATEWAY.

How can I do to fix this?
And in Wordpress admin, my website URL should be http://example.org/blog or https://example.org/blog?

Thanks a lot!