The 25-year-old midfielder has put pen to paper on a four-year deal for an undisclosed fee, keeping him at the Amex Stadium until 2021.
Gross will officially join the Seagulls on June 10, becoming the club's first signing since they won promotion to the Premier League.
"We are delighted that Pascal has opted to sign for us, amid interest from a number of clubs from the Premier League and across Europe, and I am pleased to welcome him to the club," manager Chris Hughton told the club's official website.
"He offers something different to our existing midfielders, as an attacking midfielder in a more advanced position, operating behind the forward line; he will give us a different and new option going into the new season."
Gross is expected to make his final appearance for Ingolstadt when they host Schalke 04 in their last game of the season on Saturday.