Steinhaus - the partner of English ex-Premier League and World Cup referee Howard Webb - has refereed second-tier games for six years.
"I am aware that I will be the first female referee in the Bundesliga and will be closely watched by the media and the public," Steinhaus said.
"For us all, it's a dream come true. I'm very much looking forward to the task that awaits me," she added.
Webb, who is now leading efforts to introduce video technology to Major League Soccer, said he was "absolutely thrilled to bits" and believes it could help to inspire more women to reach the top level.
He told BBC Radio 5 live he did not think it would be too long before the Premier League had female officials taking charge of games.
"We have some good female officials in England, more and more are coming through and if they have the ability it shouldn't make any difference if they are male or female," he added.
Steinhaus has faced scrutiny already in German football and admitted: "I have worked very hard for this in the last few years and suffered a few setbacks."
When fourth official at a Bayern Munich match in October 2014, then Bayern coach Pep Guardiola put his arm around her shoulders as he argued about a refereeing decision. She brushed his arm off but the Spaniard was subsequently criticised in the media.
Fortuna Dusseldorf midfielder Kerem Demirbay was banned for five games in 2015 for saying "women have no place in men's football" after Steinhaus sent him off for a second bookable offence.
He later apologised but was ordered by his club to referee a girls' football match as punishment.
DFB president Reinhard Grindel said: "Hopefully the first female referee in the Bundesliga is an incentive for many young girls in this country to try to emulate her."
Steinhaus will referee the Women's Champions League final between Lyon and Paris St-Germain in Cardiff on 1 June.
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