[eluser]gigas10[/eluser]
In my opinion, there is no "correct" way, just rebuild the website/application using CodeIgniter. I recently did this, I had an application that was almost 4 years old, which was written procedurally and with no framework. I just had to rebuild the entire application with CodeIgniter.
The application originally totaled 22,000 lines of code and with CodeIgniter, I wrote only 6,000 lines. You can see how much effort this would have saved me from the beginning. The original write of the application took me 2 weeks, the rewrite took me 3 days. Also, the code is way more maintainable then before.