The 30-year-old had been with the German side for the last two seasons, playing 41 times in the Bundesliga, but he was unable to stop them from being relegated last season.
He has signed a three-year deal with the Seagulls and has joined up with his new side at their training camp in the Austrian Alps.
Suttner, capped 18 times by Austria, had spent the remainder of his career with Austria Vienna, coming through their youth ranks and going on to make more than 250 senior appearances for the club.
He becomes the second Ingolstadt player to join Brighton ahead of their first season in the Premier League, boss Chris Hughton having also signed midfielder Pascal Gross over the summer.
"Markus is someone we have been aware of for some time," Hughton told the club's official website.
"I am pleased we have managed to complete the transfer at this stage, and he is now able to join us for the second half of the week.
"He has a great level of experience internationally, and in the top divisions in both his native Austria and Germany, where he has played the last two seasons with Ingolstadt, and that experience will serve us well.
"He will add competition at the back on the left side of defence, and I'm now looking forward to working with him."
Suttner said: "In this stage of my career, it's perfect to play in the Premier League, and the challenge for Brighton is a similar one to the one I first encountered with Ingolstadt.
"For me, the chance to play in the Premier League is one of the best options for any player and I'm very happy to be here.
"It's a very good move at this time in my career, and I don't have words to describe how happy I am to have signed the contract."
Suttner is Hughton's fourth addition, with Gross and Valencia goalkeeper Matthew Ryan joining their senior squad while Celtic youngster Josh Kerr links up with their U23 squad.
