Selke, who only signed a contract extension at Bremen until 2018 in September, pens a five-year deal at Leipzig that runs until 2020.
The 20-year-old forward moves to the second-tier side, who have enjoyed a rapid rise through the leagues in Germany on the back of substantial financial backing, for an undisclosed fee and is excited about his new challenge.
"For me, this new chapter starts only in the summer," he said. "Until then I would like to play my best for the rest of the season.
"I thank Werder for their cooperation in recent years. Here I was able to develop and I've made a big step forward.
"From the summer I want to help a very ambitious club to be successful. I thank Werder that they allow me this step in my career."
Selke's decision to move out of the Bundesliga may come as a surprise considering his form at last year's Under-19 European Championship - in which he struck 11 goals in 10 games - led to rumours of a switch to one of Europe's top clubs.
However, Bremen general manager Thomas Eichin stated that the move made sense for all parties and believes Selke will soon return to the Bundesliga with Leipzig.
"We have always said that we conduct such negotiations where all parties benefit," he said. "Davie has opted for a sporting concept in Leipzig which will lead to him sooner or later playing in the Bundesliga again and the economic environment is very attractive."
Selke has scored six goals in 23 Bundesliga appearances this term.
