The privately-owned toymaker, which has recovered from near-collapse 13 years ago, saw slowing growth in the second half of last year as profits returned to a more "sustainable" level after years of double-digit growth.
In a statement, Mr Knudstorp said Mr Padda, who has worked at the company for 15 years, played an "integral role in the turnaround" and created a "solid foundation from which to continue to transform the company".
Mr Christiansen, who is 51-years-old starts as chief executive in October, said he has "loved building with Lego bricks" since he was a child.
"As I look at the challenges facing this generation of children, the group's mission, to inspire and develop the builders of tomorrow, is more important and urgent than ever," he said.