This sentence is formal. You can use it to show your appreciation in front of people in an official occasion.
This ’次第' means 'how things have gone'. You've been feeling thankful for something, and you've decided to express it because you've got a chance to speak in front of people you are feeling thankful to. This '次第' means this sequence of events.
I think that you can 'わけ(訳)', which sounds rather casual, instead of this '次第'.