The Manchester City winger was a prime target for most European big guns in the close season as they all failed to strike a deal for his services.
Speaking after a goalles draw with Barcelona in the Champions League opener on Tuesday, Sancho stressed he is eyeing more success with the Signa Iduna outfit.
"I can't tell the future. I just take it game by game. I just wanna give 100 per cent for Borussia Dortmund.
"I really wanna do well with Dortmund. Obviously I want to win titles and give everything.
"It's crazy. Everything has come so fast," Sancho told Viasat. "But I have a great team. They keep me humbled. I just take it game by game and give 100 per cent."
The 19-year-old has been touted as one of the prominent stars in his position after departing Manchester City in 2017 for a reported £8 million.
And since his arrival, Sancho has been impressive in the Bundesliga as his thirty-four appearances last season recorded 12 goals with fourteen assists, helping Dortmund finish second in the league table.
After four games so far, Dortmund occupy the second position in the table, two points adrift leaders RB Leipzig.