The goal came after just seven minutes in Valencia after great link-up play between Helen Richardson-Walsh, Sophie Bray and goalscorer Lily Owsley.
Great Britain had chances to double their lead but were denied by Germany goalkeeper Kristina Reynolds.
And GB goalkeeper Maddie Hinch made a number of late saves.
She said: "Words can't really describe the feeling. To reach a final and book a spot at Rio, we can't be happier."
Owsley's first goal in the competition ensured Danny Kerry's side remain unbeaten in the World League and will face China in Sunday's final.
"For 15 minutes we were awesome. After that we won ugly," Kerry said.
The top three teams in the World League qualify for next year's Olympics and by winning the semi-final it guaranteed GB's passage to Rio.
Great Britain's women have qualified for the 2016 Rio Olympics after beating Germany 1-0 in the semi-finals of hockey's World League.