Burley has signed a four-and-a-half-year deal with the Scottish Football Association after a compensation package was agreed with Southampton.
The experienced manager emerged as the leading contender from a four-man shortlist which also included Mark McGhee, Graeme Souness and Tommy Burns.
And the former Ipswich and Hearts boss admitted that he was shocked to emerge from what he felt was an extremely strong pool of candidates.
Speaking at a Hampden Park press Burley said: "It's a great honour, it's something you want to do, given the opportunity. I never thought that it would ever happen.
"When Scotland showed interest, there were so many excellent candidates with huge experience.
"To be asked to be manager of my country is a great honour, and something I'm really looking forward to.
"I think at this stage of my career after being a manager for almost 16 years now, I feel I'm ready for it. I'm very pleased the SFA have showed faith and belief in giving me the job.
"I'm really looking forward to it. I was surprised to get the job. But maybe they've (the SFA) seen something that will help Scotland.
"I feel it's the right time for me and hopefully I can be a successful Scottish manager."