A 38-year-old police officer, Steinhaus will referee the 2017 Women's Champions League final between Lyon and Paris Saint-Germain on June 1.
She has also worked in the second division of the Bundesliga for a decade.
"When Lutz Michael Fröhlich [the head of German referees] informed me, I was quite speechless", Steinhaus told the official German Football Association [DFB] on Friday.
The Bundesliga will feature a female referee for the first time next season.
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I said before I'd love to score the winning goal and for it to happen is brilliant. We've got the team, we've got the belief, so next season hopefully it's our year".
"It has always been my dream to be a Bundesliga referee".
The first female referee in German professional football, Steinhaus has refereed at several high profile tournaments in women's football, while she also oversaw the women's gold medal football match between the United States and Japan at the 2012 Olympics. According to Newsweek, neither the Premier League or Spain's La Liga have ever allowed a woman to act as the main referee, which unlike other in sports is the sole official on the field of play during a match.
Steinhaus has refereed second-tier games for six years. I am used to this pressure and am convinced I will find my feet quickly.
Martin Petersen, Sven Jablonski and Soeren Storks will join the Bundesliga from August along with Steinhaus while Wolfgang Stark, Guenter Perl and Joachim Drees step down due to age limits. Steinhaus coolly brushed him off, while German media heavily criticized the Spaniard, who now manages Manchester City.