The German Football Association (DFB) announced the news with Steinhaus - the first female professional referee in German football - having overseen games in the 2. Bundesliga since 2007.
Steinhaus has officiated at international level since 2005. She took charge of the 2011 FIFA Women's World Cup final and the showpiece of the women's football tournament at the 2012 Olympic Games.
A 38-year-old police officer, Steinhaus will referee the 2017 Women's UEFA Champions League final between Lyon and Paris Saint-Germain on June 1.
And she has now made further history with her promotion to the German top flight.
Speaking to the DFB's official website, Steinhaus said: "[Referees chief] Lutz Michael Frohlich and his team are in constant exchange with us referees. That's why I was not particularly surprised when he called me on Wednesday.
"When he informed me in our telephone call about the decision of the referee's commission, I was quite speechless."
Asked about her emotions upon receiving the news, Steinhaus replied: " Disbelief, joy, happiness, relief, curiosity, I do not know. It was simply a turbulent roller coaster ride of emotions.
"It has always been my dream to referee in the Bundesliga. That this dream is to become true now naturally fills me with great joy.
"It is on the one hand confirmation for the hard work I've done to get here, on the other hand also great incentive to continue to work.
"I'm really looking forward to the task that awaits me. Certainly, as a referee, I am under special scrutiny at the beginning of the season - even through the media.
"I would hope that the current developments will also have a positive impact on newcomers [female referees], or those who want to become one."