Campania-born Immobile will be among the 23 players travelling to Brazil to represent Italy at the World Cup finals but left the Azzurri training camp to travel to Germany earlier on Monday.
He had been playing for Torino under a co-ownership arrangement with Italian champions Juventus and previously spent time with Genoa and at Pescara.
He was named Serie B player of the year in 2012 having helped Pescara win promotion with his personal haul of 28 league goals.
And before Immobile had undergone a successful medical in Dortmund, Torino president Urbano Cairo told Gazzetta dello Sport: "We listened to Immobile's wishes. It was a difficult situation as half of the player's sporting rights are owned by Juventus.
"He has received a very important offer. At Torino he earns 800,000 euros (per year) while Borussia have offered him three times that amount, plus a bonus. For us it was an untenable figure."