How to transfer Blog to different host

I’ve my blog https://ms.delivi.info/ hosted in a Free Webspace, now I want to move to my new hosting account, I can change the domain nameserver only after the entire blog is transferred and setup.

I coped all the wordpress files and dtabase tables from my old hosting account to the new one, but since I didnt change the name server for my domain, I’m accessing the blog from a different URL to check wheter it is functioning properly or not, but it results in a 404 error page. Please help me, is there any automatic method to transefer settings from onew host to another.