The co-frontman of the four-piece reunited with Pete Doherty, John Hassall and Gary Powell for recent shows in London, Leeds and Reading.
In a mailout to fans, Barat said: "I would like very much to thank you for your hardy support for The Libertines over the last week.
"It has been truly beyond words and I couldn't have been happier with your response. I am predictably exhausted but exhilarated and so glad to have been a part of it once more."
He added: "I write this from Brussels where I am talking to a great many people about my new record and I am happy to say it has being splendidly received.
"I can't quite believe I'm back on the horse already and will be back here touring the new material in only a matter of weeks. Needless to say it will be grand and I hope to see many of the old faces."