Hello,
As far as I know the easiest way (and the right one) is to get the hiring letter from employer and then contact the embassy in your country.
You should not come to Sri Lanka under a tourist visa as you would not be able to convert it to work permit once you are here.
Please read this :
Important
To obtain a Residence Visa, it is necessary to arrive in Sri Lanka on an Entry Visa issued by a Sri Lankan Mission abroad with the concurrence of the Controller General of Immigration and Emigration. The fact that you wish to apply for Sri Lankan Residence Visa has to be mentioned when obtaining the entry visa and necessary supporting documents has to be submitted.
This is an extract from this page :
A BOI company would help for sure but is not necessary normally.
Good luck!
Julien