Two years after the events of Thor, one year after the events of Avengers.
This was discussed in an interview with Kevin Feige, as being about a year or so:
That leads me to suggest you are keeping a time line in your mind with these movies. We know Iron Man 3 took place six months after The Avengers. Jane mentions that Thor 2 happens like two years after the original and Scarlett Johansson recently said The Winter Soldier is like two years after The Avengers. So Thor centric, where does Thor 2 take place after The Avengers? How long has he been away? We see almost the next scene after with the Loki scene.
Yeah. You know, we think it’s been at least a year from the end of The Avengers and that between Loki being sentenced to the dungeons and Thor finishing up putting out the fires between the nine realms that it’s been about a year, but it’s probably been a year before that since he was in New Mexico with Jane, so that’s the two years.
There was also an interview in Empire with Craig Kyle (the producer) who said it was about two years since the events of Thor, one year since the events of The Avengers. (Unfortunately, I can't find a link).
I think the scene with Odin reprimanding Loki takes place very shortly after The Avengers, and then time passes while Thor does the rounds.
There was a two-issue prelude comic to Thor 2 from Marvel which includes that scene, and has it set immediately after Thor and Odin return to Asgard with the Tesseract at the end of The Avengers (that comic also shows the reconstruction of the Bifrost, and shows the dark magic Odin uses to send Thor to Earth).