How does SQL Server Startup?
Ah, after you updated your comment I realized that you were asking about how to start another process after all databases have been restored/loaded. You can configure a stored procedure to be called using the sp_procoption. I am pretty sure that runs after all databases are ready. Next, you just need to invoke your external process via sql server.

"...Execution of the stored procedures starts when all databases are recovered and the "Recovery is completed" message is logged at startup...."