Since Blogger (blogspot) isn't an actual hosting company, there's no real way to transfer the site from Blogger to your account with us directly.
However, Blogger has a feature which will allow you to export your site content to a more universal format.
They have a FAQ entry on how to accomplish it here.
WordPress does support importing directly from your blogger account:
Simply install WordPress from MOJO Marketplace in your cPanel.
Then in your WordPress Admin area (example.com/wp-admin), go to Manage → Import → Blogger and follow the directions to complete the import.
Recommended Help Content
How to Migrate a self hosted copy of WordPress
How to manually migrate a WordPress site, not using ManageWP.
How to move WordPress from one folder to another folder on the same server.
Related Help Content
I am trying to transfer a domain(s) from my current registrar to justhost. When I fill out the transfer form I cannot get beyond step 2/4. There does not seem to be any "submit" or "next"
If you have a WordPress blog hosted on WordPress.com, you can easily export it and import it to WordPress that is installed on your hosting account with justhost. Login to the WordPress Data
There are multiple reasons why a domain transfer may fail. This article explains several reasons why your transfer may be unsuccessful and what you can do to fix it.
This article will explain how to login to a WordPress site using WordPress tools.
This article explains how to prepare your domain to be transferred from Just Host to a new registrar. You'll initiate the transfer itself with the gaining registrar, but there are a few things you can do to ensure the process goes smoothly.
This article will explain how to change the Site URL or Home URL setting in WordPress. This may be useful if you have moved your WordPress site or are planning to move your WordPress site.
Maintaining your domain registration and hosting services within the same account allows you to manage both services with only one login password, making it easier for you to stay on top of everything related to your website. This article explains the process to transfer your domain to [% provinfo.n
Learn how to use WordPress, WordPress started as just a blogging system, but has evolved to be used as full content management system and so much more through the thousands of plugins, widgets, and themes now available.